Hyperthermia and High Dose Rate Radiation Therapy in Treating Patients With Recurrent Prostate Cancer After Radiation

Inclusion Criteria: * Male age \>= 18 years * Karnofsky performance status \> 70% * Expected survival of at least 3 years * Informed consent signed by the subject * PSA blood test within 60 days prior to registration * Prostate biopsy with Gleason score and TNM staging within one year prior to registration * No evidence of metastasis on computed tomography (CT) or magnetic resonance imaging (MRI) of the pelvis within 120 days prior to registration * No evidence of metastasis on bone scan within 120 days prior to registration * Within 60 days prior to registration, hematologic minimal values: absolute neutrophil count \> 1,500/mm\^3 * Within 60 days prior to registration, hematologic minimal values: hemoglobin \> 8.0 g/dl * Within 60 days prior to registration, hematologic minimal values: platelet count \> 100,000/mm\^3 * Men of childbearing potential must be willing to consent to using effective contraception while on treatment and for at least 3 months after completion of treatment * Histologically proven persistent or recurrent adenocarcinoma of the prostate following prior external beam radiation therapy or brachytherapy * Prior androgen deprivation or chemotherapy is allowed if discontinued at least 30 days prior to enrollment * Concurrent disease - patients under treatment for concurrent medical conditions will be eligible for protocol treatment if, in the opinion of the physician responsible for hyperthermia treatment that the concurrent medical condition will neither interfere with the process of the treatment or patient assessments nor add significantly to the risks or complications of the treatment Exclusion Criteria: * History of urological surgery or procedures predisposing to genitourinary (GU) complications after radiation, i.e., anastomoses, stricture repair, transurethral resection, etc. (will be determined by radiation oncologist) * Prior thermal ablative therapy for prostate cancer (e.g. high-intensity focused ultrasound \[HIFU\] or cryoablation) * Documented distant metastatic disease * Patient with other co-morbidities that in the opinion of the treating physician would be a contra-indication to protocol participation (e.g. inflammatory bowel disease) * Mental incompetence or criminal incarceration