B737-800 pilot reported numerous Engine Fire/Overheat Warnings during push back. The flight crew requested ARFF to inspect the aircraft and were towed back to the Gate for Maintenance. There were no signs of Engine Fire and no evacuation.

Narrative

On ramp. After Push Back/Push Crew disconnected and no longer present. Engine #2 running; Engine #1 being started; the Master Fire Warnings Illuminated with no other indications. Master Fire Warnings extinguished on their own after 20-30 seconds. After #1 engine stabilized; both Master Fire Warnings Illuminated again and stayed on. Both engines were shut down. Master Fire Warnings were reset and stayed out. Informed flight attendants about Fire indications over cabin interphone; that I expected an anomaly (Possibly no Fire); but to be alert for Fire indications and let me know. They reported no abnormalities at that time. Reported Fire indications to Airport Tower; asked if they saw visible smoke etc... and requested ARFF. Told Tower and ARFF Fire indications were not typical and possibly an anomaly. Informed Passengers and Crew of abnormal aircraft system indication; to expect safety equipment; and that we would be returning to the Gate. Flight Attendants informed me of a slight overheat smell at row XX after engines shut down. I explained indications to ARFF Crew Chief; requested they inspect entire aircraft (engines; APU and cargo compartment). After they deemed aircraft safe to return to Gate; we were towed back in; ground electric power established; APU shut down; Passengers deplaned (normal deplaning) while aircraft re-inspected by ARFF. Fire Chief reconfirmed aircraft safe; no fire/overheat. To note; I did not use the words Mayday/Emergency with ATC; however was implied via my direct comms/request for ARFF. Response was immediate. First Officer (FO) worked comms with Operations; Maintenance and Dispatch; while I communicated with ARFF and ATC. Possible aircraft system malfunction or overheat. Recommend discrete VHF frequency be assigned for ARFF/ATC Ground Control comms. My comms seemed to interfere/were impeded by/with normal ground control comms.