The investigators want to find out if the drugs Velcade and temsirolimus given together are effective in treating cancer. Velcade and temsirolimus are each FDA approved individually for certain types of cancer (Velcade for multiple myeloma and mantle cell lymphoma, and temsirolimus for renal cell carcinoma) but are not currently approved in combination for B-cell non-Hodgkin lymphoma. The investigators are trying to find out if giving these 2 drugs together will improve the period of time that the patient's cancer is stopped or slowed from growing and causing symptoms.

Inclusion Criteria:

• Relapsed or refractory B-cell non-Hodgkin lymphoma which includes: diffuse large B-cell lymphoma; primary mediastinal large B-cell lymphoma; follicular lymphoma (grade 1, 2 or 3); mantle cell lymphoma; small lymphocytic lymphoma; marginal zone lymphoma; lymphoplasmacytic lymphoma; B-cell lymphoblastic lymphoma; or Burkitt lymphoma. "Grey-zone" lymphomas must be approved by the Wisconsin Oncology Network (WON) Study Chair or Principal Investigator prior to enrollment.
• At least one measurable tumor mass (>1.5 cm in the long axis and > 1.0 cm in the short axis) that has not been previously irradiated, or has grown since previous irradiation.
• Documented relapse or progression following prior antineoplastic therapy.
• No clinical or documented radiographic evidence of central nervous system lymphoma.
• Eastern Cooperative Oncology Group [ECOG] performance status of 0-2.
• The following clinical laboratory values within 14 days prior to enrollment:
• Absolute neutrophil count (ANC) ≥ 1.5 x 109 cells / L
• Platelets ≥ 100 x 109 cells / L
• Alanine transaminase (ALT) and Aspartate transaminase (AST) ≤ 3X the upper limit of normal (ULN)
• Total bilirubin ≤ 2X the upper limit of normal (ULN).
• Calculated creatinine clearance ≥40 mL/min (using the Cockcroft-Gault equation).
• Female subjects must be either post-menopausal for at least 1 year or surgically sterilized, agree to practice 2 effective methods of contraception from the time of signing the informed consent form through 30 days after the last dose of Velcade, or agree to completely abstain from heterosexual intercourse.
• Male subjects, even if surgically sterilized (ie, status postvasectomy) must agree to 1 of the following: practice effective barrier contraception during the entire study treatment period and through a minimum of 30 days after the last dose of study drug, or completely abstain from heterosexual intercourse.

Exclusions:

• Antineoplastic, experimental, or radiation therapy within 14 days prior to enrollment, or 21 days prior to Day 1 of Cycle 1.
• Radioimmunoconjugates within 10 weeks of Day 1 of Cycle 1.
• Autologous stem cell transplant within 3 months before Day 1 of Cycle 1, or any prior history of allogeneic stem cell transplant.
• Platelet transfusion within 7 days of Day 1 of Cycle 1.
• Ongoing therapy with glucocorticoids. Prednisone ≤15 mg per day or its equivalent is allowed.
• Patient has Grade 2 or greater peripheral neuropathy within 14 days before enrollment.
• Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure (see section 8.4), uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities.
• Patient has hypersensitivity to Velcade, boron or mannitol.
• Female subjects that are pregnant or breast-feeding.
• Serious medical or psychiatric illness that is likely to interfere with participation
• Diagnosed or treated for another malignancy within 2 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy.
• Prior therapy with both Velcade and temsirolimus. Patients who have previously been treated with either Velcade or temsirolimus (but not both) are eligible.
• Radiation therapy within 3 weeks before randomization.
• Patients must not be taking the following strong CyP3A inducers at study entry: phenytoin, phenobarbital, rifampin, carbamazepin, rifabutin, rifampicin, a one week washout period is required.