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…