Combination of Temsirolimus and Sorafenib in the Treatment of Radioactive Iodine Refractory Thyroid Cancer

Inclusion Criteria: * Patients must have histopathologically confirmed at MSKCC thyroid carcinoma of follicular cell origin (D-TC-FCO), which includes papillary, follicular, Hürthle cell histology, or anaplastic along with their respective variants. * Available pathology for RAF mutational testing (e.g., paraffin block or 5-10 unstained slides). It is not required that mutational testing be completed before starting the clinical study. * Patients must have surgically inoperable and/or recurrent/metastatic disease. * Patients must have a PET scan prior to the protocol start date and have at least one FDGavid lesion that has not been removed surgically or radiated (unless it has progressed by RECIST criteria after the completion of radiation therapy and is still FDG-avid). FDGavidity will be defined as any focus of increased FDG uptake greater than normal activity with SUV maximum levels greater than or equal to 3. PET scan can have been done at any time prior to the start of therapy, although it is recommended that it be done within 3 months prior to the start of therapy. * Patients must have measurable disease by RECIST criteria, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 20 mm with conventional techniques or as ≥ 10 mm with spiral CT scan; performed ≤ 4 weeks of protocol start date. * Patients must have progressive disease defined by at least one of the following occurring during or after p…