Background: * Cisplatin-containing chemotherapy is the standard of care for advanced thymoma and thymic carcinoma that cannot be treated with surgery. New options for treatment are necessary in patients with advanced thymoma and thymic carcinoma that have progressed on cisplatin-containing therapy. * IMC-A12 is a new (experimental) agent that has not yet been approved by the Food and Drug Administration. IMC-A12 blocks the Insulin-like Growth Factor 1 receptor (IGF-1R). IGF-1R is found on many types of cancer cells, including cancer of the thymus, and is thought to play an important role in helping these cells to grow and divide. Objectives: * To determine if IMC-A12 has an effect on tumor growth in patients with cancer of the thymus. * To evaluate the safety and tolerability of IMC-A12 in treatment for cancer of the thymus. Eligibility: \- Individuals older than 18 years of age who have cancer of the thymus (thymoma, thymic carcinoma, or thymic carcinoid tumors) that has progressed in spite of standard treatment. Design: * Treatment will take place in 21-day cycles. Patients will receive one dose of IMC-A12 intravenously once every 3 weeks at the Clinical Center. During the Clinical Center visits, researchers will perform study tests and procedures to see how the study drugs are affecting the body. * Patients will undergo a number of tests and procedures during the treatment cycle, including physical examinations, blood and urine samples for standard tests, imaging studies (ultrasound, magnetic resonance imaging (MRI) or computed tomography (CT) scans) to evaluate tumor growth, and blood and urine samples to evaluate the amount of IMC-A12 in the body. * Patients may continue to take the drug as long as there are no adverse side effects and as long as the tumor does not grow.

Background: Cisplatin-containing chemotherapy is the standard of care for advanced unresectable thymoma and thymic carcinoma. New options for treatment are necessary in patients with advanced thymoma and thymic carcinoma that have progressed on cisplatin-containing therapy. The insulin-like growth factor (IGF) pathway is being studies in various malignancies including thymoma and thymic carcinoma. IMCA12 is an anti-IGF-1R monoclonal antibody that has shown activity in patients with thymic malignancies. Objectives: * To determine the objective response rate (partial response (PR)+complete response (CR)) to IMC-A12 monotherapy in patients with advanced or recurrent thymoma or thymic carcinoma. * To evaluate time to response, duration of response, progression-free survival (PFS) and overall survival (OS) * To assess safety of IMC-A12 * To perform immunohistochemistry for IGF1R expression on tumor samples of thymoma and thymic carcinoma (exploratory) * To correlate response to therapy with changes in fludeoxyglucose 18F-positron emission tomography (FDG-PET) imaging at baseline and first restaging * To perform pharmacokinetic (PK) analysis of IMC-A12 * To perform pharmacodynamic (PD) analysis in blood for the detection of IGF1R, AKT and pAKT in peripheral blood mononuclear cells (PBMC's) (exploratory). * To assess circulating endothelial cell, circulating endothelial progenitor cells, immune subset analysis and glucose transport in peripheral blood monocytes and lymphocytes (exploratory). * To evaluate anti-cytokine antibodies in peripheral blood (exploratory). Eligibility: * Patients with histologically confirmed thymic carcinoma or thymoma who have previously been treated on at least one platinum-containing chemotherapy regimen * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Adequate renal, hepatic and hematopoietic function * No major surgery, radiotherapy, chemotherapy or biologic therapy within 28 days of IMC-A12 therapy Design: * Patients will receive IMC-A12 at a dose of 20 mg/kg intravenously once every three weeks * Treatment with IMC-A12 alone will continue until disease progression * Toxicity will be assessed every cycle by Common Terminology Criteria for Adverse Events (CTCAE) Version 3.0 until December 31, 2010, and by CTCAE Version 4.0 beginning January 1, 2011 * Tumor response assessments by RECIST 1.0 criteria will be performed every 2 cycles * Correlative studies including tissue immunohistochemistry studies will be done on existing tumor blocks * Blood samples will be collected for for PK's, PD's, circulating endothelial cells (CEC's), circulating endothelial precursor cells (CEPC's), immune subsets, glucose transport and cytokine antibodies.