INCLUSION CRITERIA

        -Patients must be greater than or equal to 12 months and ≤ 21 years of age at the time of
        study enrollment.

        Patients must have one of the following:

        Leukemia

          -  Patients must have relapsed or refractory acute lymphoblastic leukemia (ALL) with
             greater than or equal to 25% blasts in the bone marrow (M3). OR

          -  Patients may have an M2 marrow (greater than or equal to 5% to < 25% blasts) with an
             extramedullary site of relapse; including CNS 2 and CNS 3.

          -  Refractory disease defined as no more than 1 prior failed salvage attempt following
             the current relapse, or no more than 2 additional treatment cycles after initial
             induction failure in newly diagnosed patients.

        Lymphoma

          -  Patient must have relapsed or refractory lymphoblastic lymphoma or peripheral T-cell
             lymphoma.

          -  Patient must have histologic verification of disease at original diagnosis.

          -  Patient must have evaluable or measurable disease documented by clinical or
             radiographic criteria or bone marrow disease present at study entry.

          -  Patients may have CNS 2 or 3 disease, if other sites of involvement.

        Karnofsky greater than or equal to 50% for patients > 16 years of age and Lansky greater
        than or equal to 50 for patients ≤ 16 years of age.

        Patients must have fully recovered from the acute toxic effects of all prior anti-cancer
        chemotherapy.

        Patients must have had 2 or more prior therapeutic attempts defined as:

          -  Relapse after going into remission from re-induction for the first or subsequent
             relapse (ie: 2nd , 3rd, 4th…relapse), or

          -  Patients with lymphoma may have refractory disease after first or greater relapse and
             a single re-induction attempt.

        Patients with leukemia or lymphoma who relapse while receiving maintenance chemotherapy
        will not be required to have a waiting period before enrollment onto this study.

        At least 14 days must have elapsed after the completion of cytotoxic therapy, with the
        exception of hydroxyurea.

        Hematopoietic growth factors: At least 14 days after the last dose of a long-acting growth
        factor (e.g. Neulasta) or 7 days for short-acting growth factor.

        Biologic (anti-neoplastic agent): At least 7 days after the last dose of a biologic agent.
        For agents that have known adverse events occurring beyond 7 days after administration,
        this period must be extended beyond the time during which adverse events are known to
        occur. The duration of this interval must be discussed with the study chair

        Immunotherapy: At least 42 days after the completion of any type of immunotherapy, e.g.
        tumor vaccines. or chimeric antigen receptor T cell (CART) therapy.

        Monoclonal antibodies: At least 3 half-lives of the antibody must have elapsed after the
        last dose of a monoclonal antibody. (ie: Rituximab = 66 days, Epratuzumab = 69 days).
        Patients must have been off blinatumomab infusion for at least 7 days and all drug-related
        toxicity must have resolved to grade 2 or lower as outlined in the inclusion and exclusion
        criteria

        XRT: At least 14 days after local palliative XRT (small port); At least 84 days must have
        elapsed if prior TBI, craniospinal XRT or if greater than or equal to 50% radiation of
        pelvis; At least 42 days must have elapsed if other substantial marrow radiation.

        Stem Cell Infusion: No evidence of active graft vs. host disease and at least 84 days must
        have elapsed after transplant or stem cell infusion.

        Study specific limitations on prior therapy: Patient may not have received therapy with an
        mTOR inhibitor.

        Adequate Bone Marrow Function Defined as: Blood counts are not required to be normal prior
        to enrollment on trial. However, platelet count must be greater than or equal to 20,000/mm3
        to initiate therapy (may receive platelet transfusions). Patients should not be known to be
        refractory to red blood cell or platelet transfusions.

        Adequate Renal Function Defined as:

          -  Creatinine clearance or radioisotope GFR greater than or equal to 70ml/min/1.73 m2 or

          -  Normal serum creatinine based on age and gender.

        Adequate Liver Function Defined as:

          -  Total bilirubin (sum of conjugated + unconjugated) must be less than or equal to 1.5 x
             normal per institutional normal values for age.

          -  SGPT (ALT) and SGOT (AST) must be less than 3 x institutional upper limit of normal
             (Grade 1 or less per CTCAE 4).

             --GGT must be less than 2.5 x institutional upper limit of normal (Grade 1 or less per
             CTCAE 4).

          -  Serum albumin greater than or equal to 2 g/dL.

          -  The hepatic requirements may be waived for patients with elevations clearly due to
             leukemic infiltration after consultation with the Study Chair or Vice Chair.

          -  Fasting or non-fasting serum triglyceride level ≤ 300 mg/dL and serum cholesterol
             level ≤ 300 mg/dL.

        Adequate Cardiac Function Defined As:

          -  Shortening fraction of ≥ 27% by echocardiogram, or

          -  Ejection fraction of ≥ 50% by gated radionuclide study.

        Adequate Pulmonary Function Defined as:

          -  Pulse oximetry > 94% on room air (> 90% if at high altitude)

          -  No evidence of dyspnea at rest and no exercise intolerance.

          -  Baseline chest x-ray with no evidence of active infectious disease or pneumonitis.

        Reproductive Function

          -  Female patients of childbearing potential must have a negative urine or serum
             pregnancy test confirmed prior to enrollment.

          -  Female patients with infants must agree not to breastfeed their infants while on this
             study.

          -  Male and female patients of child-bearing potential must agree to use an effective
             method of contraception approved by the investigator during the study.

          -  Random or fasting glucose within the upper limits of normal for age. If the initial
             blood glucose is non-fasting and above normal limits a fasting glucose can be obtained
             and must be within the upper limits of normal for age.

        EXCLUSION CRITERIA

          -  Corticosteroids: Patients receiving corticosteroids who have not been on a stable or
             decreasing dose of corticosteroid for at least 7 days prior to enrollment are not
             eligible.

          -  Investigational Drugs: Patients who are currently receiving another investigational
             drug are not eligible. The definition of "investigational" for use in this protocol
             means any drug that is not licensed by the FDA, Health Canada or the Therapeutic Goods
             Administration to be sold in the countries they govern. (United States, Canada and
             Australia)

          -  Anti-cancer Agents: Patients who are currently receiving or may receive while on
             therapy, other anti-cancer agents, radiation therapy or immunotherapy are not eligible
             [except leukemia patients receiving hydroxyurea, which may be continued until 24 hours
             prior to start of protocol therapy]. Intrathecal chemotherapy (at the discretion of
             the primary oncologist) may be given up to one week prior to the initiation of study
             therapy.

          -  Anti-GVHD or agents to prevent organ rejection post-transplant: Patients who are
             receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host
             disease post bone marrow transplant or organ rejection post transplant are not
             eligible for this trial. At least 3 half-lives must have elapsed after the last dose
             of GVHD meds.

          -  Anticoagulants: Patients who are currently receiving therapeutic anticoagulants
             (including aspirin, low molecular weight heparin, and others) are not eligible. At
             least 3 half-lives must have elapsed after the last dose of anticoagulants.

          -  Angiotensin-converting enzyme (ACE) inhibitors: Patients who are currently receiving
             ACE inhibitors are not eligible due to the development of angioneurotic edema-type
             reactions in some subjects who received concurrent treatment with temsirolimus + ACE
             inhibitors. At least 3 half-lives must have elapsed after the last dose of ACE
             inhibitors.

          -  Enzyme inducing Anti-convulsants: Patients who are currently receiving enzyme inducing
             anticonvulsants (ie phenytoin, phenobarbitol, or carbamazepine) are not eligible.
             Stabilizing on a non-hepatic inducing metabolizing anti-convulsant (ie: gabapentin or
             levetiracetam) prior to study entry is acceptable. At least 3 half-lives must have
             elapsed after the last dose of enzyme inducing anti-coagulants.

          -  Patients receiving treatment with azoles such as fluconazole or voriconazole which are
             potent inhibitors of temsirolimus metabolism. At least 3 half-lives must have elapsed
             after the last dose of azoles.

        Infection Criteria

        Patients are excluded if they have:

          -  Positive blood culture within 48 hours of study enrollment;

          -  Fever above 38.2 within 48 hours of study enrollment with clinical signs of infection.
             Fever that is determined to be due to tumor burden is allowed if patients have
             documented negative blood cultures for at least 48 hours prior to enrollment and no
             concurrent signs or symptoms of active infection or hemodynamic instability.

          -  A positive fungal culture within 30 days.

          -  Active fungal, viral, bacterial, or protozoal infection requiring IV treatment.
             Chronic prophylaxis therapy to prevent infections is allowed.

        Patients with Down syndrome and Fanconi Anemia are excluded.

        Patients will be excluded if they have significant concurrent disease, illness, psychiatric
        disorder or social issue that would compromise patient safety or compliance with protocol
        treatment or required observations, interfere with consent, study participation, follow up,
        or interpretation of study results.

        Patients with known optic nerve and/or retinal involvement (because it may not be possible
        to safely delay irradiation) are not eligible. Patients presenting with visual disturbances
        by history or physical exam should have an ophthalmological exam and, if indicated, an MRI
        to determine optic nerve or retinal involvement.