Temsirolimus and Imatinib Mesylate in Treating Patients With Chronic Myelogenous Leukemia

Inclusion Criteria: * Histologically confirmed chronic myelogenous leukemia (CML) * Philadelphia chromosome-positive OR Bcr-Abl-positive disease, meeting 1 of the following criteria: * Accelerated phase, defined by at least 1 of the following: * 10-19% blasts in the peripheral blood or bone marrow * At least 20% basophils in peripheral blood or bone marrow * Platelet count \< 100,000/mm\^3 (unrelated to therapy) * Platelet count \> 1,000,000/mm\^3 (unresponsive to therapy) * Increasing splenomegaly AND increasing WBC count (unresponsive to therapy) * Clonal evolution * Blast phase, defined by 1 of the following: * At least 20% blasts in peripheral blood or bone marrow * Extramedullary disease * Chronic phase, defined by all of the following: * Less than 10% blasts in peripheral blood or bone marrow * Less than 20% basophils in peripheral blood or bone marrow * Platelet count \> 100,000/mm\^3 * Absence of clonal evolution * May have received and/or failed prior imatinib mesylate therapy * Patients not previously treated with imatinib mesylate receive oral imatinib mesylate once daily 14 days before beginning study drug * Must be able to tolerate 600 mg per day of imatinib mesylate before starting CCI-779 * Patients with chronic phase disease must have failed prior imatinib mesylate at a dose ≥ 600 mg/day, as defined by 1 of the following: * Must not have achieved or must have lost hematologic response within 3 months after the start of imatinib mesylate * Must not have achieved or must have lost cytogenetic response after 6 months of treatment with imatinib mesylate * Must not have achieved or must have lost major cytogenetic response after 12 months of treatment with imatinib mesylate * Must have lost complete cytogenetic response * Bone marrow aspirate and biopsy with cytogenetics and fluorescent in situ hybridization confirming t(9;22) completed within the past 28 days * Performance status - SWOG 0-2 * More than 3 months * See Disease Characteristics * Bilirubin normal * AST and ALT \< 2.5 times upper limit of normal (ULN) (5 times ULN if suspected liver involvement with leukemia) * Creatinine normal * Creatinine clearance \> 60 mL/min * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * Ejection fraction ≥ 50% by echocardiogram or MUGA scan for patients with known positive cardiac history (e.g., heart failure, coronary artery disease, cardiomegaly on prior chest x-ray, or valvular heart disease) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Fasting cholesterol ≤ 350 mg/dL * Fasting triglycerides ≤ 400 mg/dL * No history of allergic reaction attributed to compounds of similar chemical or biologic composition to temsirolimus or imatinib mesylate * No active or ongoing infection * No psychiatric illness or social situation that would preclude study compliance * No other active malignancy except nonmelanoma skin cancer * No other uncontrolled illness * At least 48 hours since prior interferon alfa for CML * At least 6 weeks since prior stem cell transplantation * No concurrent biologic agents * No concurrent prophylactic colony-stimulating factors * At least 24 hours since prior hydroxyurea for CML * At least 7 days since prior mercaptopurine or vinca alkaloids for CML * At least 7 days since prior low-dose cytarabine (\< 30 mg/m\^2 every 12-24 hours) for CML * At least 14 days since prior homoharringtonine for CML * At least 14 days since prior moderate-dose cytarabine (100-200 mg/m\^2 for 5-7 days) for CML * At least 21 days since prior anthracyclines, mitoxantrone, cyclophosphamide, etoposide, or methotrexate for CML * At least 28 days since prior high-dose cytarabine (1-3 g/m\^2 every 12-24 hours for 6-12 doses) for CML * At least 6 weeks since prior busulfan for CML * No concurrent hydroxyurea * No other concurrent chemotherapy * At least 7 days since prior steroids for CML * No prior organ transplantation * More than 2 weeks since prior major surgery (e.g., thoracotomy or intra-abdominal surgery) * Recovered from all prior therapy * Prior experimental therapy allowed provided completion of treatment corresponds to a duration \> 5 half-lives of the experimental drug or any known active metabolite before study * No concurrent cyclosporine * No concurrent anagrelide * No concurrent oral anticoagulants, including warfarin * No concurrent CYP3A4 inducers or inhibitors * No concurrent tacrolimus * No concurrent plasmapheresis * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational agents * No other concurrent anticancer therapies