B737 flight crew reported a malfunction with the aircraft fire detection systems. Flight crew diverted and landed uneventfully.

Narrative

While preparing for the flight; we noticed an open inbound writeup for an issue with the aircraft's fire detection system. When we arrived to the aircraft; we were met by the contract mechanic who stated that he had tested the system; and found no faults. We conferenced Maintenance Control and we all agreed that the aircraft was not safe to fly; and they stated they would be flying a part in from ZZZ1; on a flight that arrived hours later. We obtained a day room and went to the hotel. We arrived back at the airport in time to depart at the expected departure time as given by Maintenance. Maintenance stated they had replaced a faulty part; it tested normally; and we were cleared to depart. A Maintenance Release was obtained; and we departed. Most of the flight was uneventful until we approached TOD (Top of Descent) for ZZZ. While at FL400; in clear; smooth air; both engines; and the APU fire warnings sounded; including the fire bell; Master Caution; and also associated Overheat lights. Each of the warnings was cycling on and off; at approximately 2-second intervals. At times; we were able to clear the warning; only to have it reappear seconds later. I transferred control to the FO (First Officer); and I referenced the FM (Flight Manual) for guidance (there wasn't any). I sent an ACARS message to Dispatch informing them of the issue and requested a phone patch with Maintenance Control (which never occurred). While waiting for a response; the FO and I agreed that ZZZ was the closest appropriate airport; and we should [request priority handling] as we have now lost the ability to detect any engine or APU fire or overheat. I [requested priority handling] with ATC and informed Dispatch of our intentions. I briefed the FAs on Brief items; but stated I did not wish them to prepare the cabin; nor did I plan to evacuate upon landing. We elected to stay at FL400 for a few minutes before starting the descent for favorable winds/groundspeed. Throughout the descent; the cycling of all of the fire warnings continued. We flew the visual approach to Runway XXL; and stopped on Taxiway 1. The FO coordinated with CFR (Crash Fire Rescue) and Airport Ops and they stated they had no indication of any fire or overheat condition; so we taxied to the gate. We requested CFR and Ops follow us to the gate. After parking; we debriefed the situation with maintenance (who met us at the gate); and I called the Chief Pilot). I then proceeded to the layover hotel.