Hyperthermic Intraperitoneal Chemotherapy With Cisplatin During Surgery or Cisplatin Before Surgery for the Treatment of Stage III or IV Ovarian, Fallopian Tube or Peritoneal Cancer

Inclusion Criteria: * Ability to understand (English-speaking), and willingness to sign a written, informed consent * Age \> 18 years old * Newly diagnosed stage III or IV epithelial (serous, mucinous, or endometrioid) ovarian, fallopian tube or peritoneal cancer diagnosed by: * Biopsy/histology (either by interventional radiology or laparoscopy) OR * Cytology; If diagnosis is based on cytology the following criteria must be met: * Immunohistochemistry on the block from cytology to demonstrate Mullerian origin * Presence of pelvic mass AND CA 125 \> 200kU/I AND CA125/CEA ratio \> 25 at initial diagnosis * Omental cake or other metastases larger than 2 cm in the upper abdomen and/or regional lymph node metastasis irrespective of size (diagnosed by computed tomography \[CT\]/magnetic resonance imaging \[MRI\], ultrasound, or laparoscopy) * Patient planned for or currently receiving neoadjuvant chemotherapy due to the fact that optimal primary CRS was determined not to be feasible by the primary surgeon * Patient must be planned or scheduled to undergo interval cytoreductive surgery after cycle 3-4 of neoadjuvant surgery * Completion of three cycles of neoadjuvant chemotherapy (NACT) with standard therapy (carboplatin \[area under the curve (AUC) 5-6\] day \[D\]1 + paclitaxel \[175 mg/m\^2\] D1 every 3 weeks) * Following 3-4 cycles of NACT partial or complete response * Following 3-4 cycles of NACT at least 50% decrease in CA-125 level between pre-cycle 1 and post-cycle 3/prior to surgery * Fit for major surgery, American Society of Anesthesiologists (ASA )1 or ASA 2 * Eastern Cooperative Oncology Group (ECOG) performance-status score of 0-2 * Serum creatinine \< 1.4 mg/dL * Creatinine clearance \> 60 ml/min (Cockcroft-Gault formula) * White blood cell count \> 3.5 x 10\^9 cells/L * Absolute neutrophil count \> 1.5 kg/ul * Platelets \> 100,000/ul * Total bilirubin within 1.5 x normal institutional limits * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x institutional upper limit of normal * For quality of life assessment, baseline questionnaires should be filled in before randomization Exclusion Criteria: * History of breast cancer or previous malignancy within 5 years prior to inclusion, with the exception of radically excised basal cell or squamous cell skin cancer or carcinoma in situ of the cervix * Low grade serious carcinoma of the ovary or borderline ovarian tumors * History or current diagnosis of inflammatory bowel disease * History of allergic reactions to compounds of similar chemical or biologic composition to cisplatin, carboplatin, and paclitaxel * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia * Patients in whom an optimal or complete cytoreduction cannot be performed will be excluded at the time of surgery and be replaced