Multicenter Phase II Study of IMC-A12 in Patients With Thymoma and Thymic Carcinoma Who Have Been Previously Treated With Chemotherapy

* INCLUSION CRITERIA: * Histologically confirmation of invasive recurrent or metastatic thymoma or thymic carcinoma by the pathology department / Center for Cancer Research (CCR) / National Cancer Institute (NCI), or the pathology department of participating institutions. * Patients must have had at least one prior platinum-containing chemotherapy regimen. There is no limit to the number of prior chemotherapy regimens received. Progressive disease should have been documented before entry into the study. * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as greater than 20 mm with conventional techniques or as greater than 10 mm with spiral CT scan. See section 11 for the evaluation of measurable disease. * Target lesions cannot be selected within previously irradiated areas, if not newly arising or clearly progressing after irradiation as proven by repeat scanning. * Patients must have recovered from toxicity related to prior therapy to at least to grade 1 (defined by CTCAE 3.0 until December 31, 2010, and by CTCAE 4.0 beginning January 1, 2011) and must not have had major surgery, radiation therapy, chemotherapy, biologic therapy (including any investigational agents), or hormonal therapy (other than replacement), within 4 weeks prior to entering the study. * Concurrent corticosteroids for myasthenia gravis, or other paraneoplastic syndromes which often accompany thymic malignancies are allowed. Inhaled steroids are also allowed. However since steroids might occasionally induce responses in thymic malignancies patients should be on a stable dose of steroids for greater than or equal to 8 weeks before enrollment in order not to confound the efficacy assessment. * Age greater than 18 years. Because no dosing or adverse event data are currently available on the use of IMC-A12 in patients less than 16 years of age, children are excluded from this study but will be eligible for future pediatric phase 1 single-agent trials. * Life expectancy of greater than 3 months. * Performance status Eastern Cooperative Oncology Group (ECOG) less than or equal to 2. * Patients must have adequate organ and marrow function (as defined below). Patients must have returned to baseline or grade 1 from any acute toxicity related to prior therapy: * leukocytes greater than or equal to 3,000/mm\^3 * absolute neutrophil count greater than or equal to 1,500/mm\^3 * hemoglobin greater than or equal to 9 g/dL * platelets greater than or equal to 100,000/mm\^3 * total bilirubin less than or equal to 1.5 times the institutional upper limit of normal (ULN) * aspartate aminotransferase (AST)(SGOT)/alanine aminotransferase (ALT)(SGPT) less than or equal to 3 times the institutional ULN (5x if LFT elevations due to liver metastases) * creatinine less than or equal to 1.5 times the institutional ULN OR --creatinine clearance greater than or equal to 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patients may be transfused to obtain a hemoglobin of 9.0. * The patient must have fasting serum glucose less than 120 mg/dL or below the institutional ULN * The effects of IMC-A12 on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study therapy and for 3 months after the last dose of IMC-A12. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Ability to comply with intravenous administration schedule, and the ability to understand and the willingness to sign a written informed consent document. INCLUSION OF WOMEN AND MINORITIES: Both men and women and members of all races and ethnic groups are eligible for this trial. Every effort will be made to recruit women and minorities in this study. EXCLUSION CRITERIA: * Patients with symptomatic brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. However, patients who have had treatment for their brain metastases and whose brain metastatic disease status has remained stable for at least 3 months without steroids may be enrolled at the discretion of the principal investigator. * Patients with poorly controlled diabetes mellitus. Patients with a history of diabetes mellitus are allowed to participate, provided their blood glucose is within the normal range (fasting less than 120 mg/dL or below institutional upper limit of normal) and if they are on a stable dietary or therapeutic regimen for this condition. * Uncontrolled medical illness including, but not limited to, ongoing or uncontrolled, symptomatic congestive heart failure (American Heart Association (AHA) Class II or worse), uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Human Immunodeficiency virus (HIV) positive patients with poorly controlled viral loads (viral load greater than 50 copies HIV/ml), and/or AIDS-defining illnesses will be excluded due to the possibility that IMC-A12 may worsen their condition and the likelihood that the underlying condition may obscure the attribution of adverse events with respect to IMC-A12. HIV positive patients with thymic malignancies not meeting the above criteria can be considered for inclusion in the study. * Patients may not be receiving any other investigational agents. * History of another invasive malignancy in the last five years. Adequately treated non-invasive, non-melanoma skin cancers, in situ carcinoma of the cervix, and surgically-removed papillary thyroid cancer will be allowed. * Prior treatment with drugs of the IGF-1R inhibitor class. * Patients with tumor amenable to potentially curative therapy as assessed by the investigator. * Pregnant women are excluded from this study because IMC-A12 is a monoclonal antibody to IGF-1R with the potential for teratogenic or abortifacient effects. IgG antibody may also potentially be secreted in milk and therefore breastfeeding women should be excluded. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to IMC-A12.