Captain reported receiving engine overheat and fire warning system indications which resulted in return to departure airport.

Narrative

While operating Aircraft X ZZZ-ZZZ1; at approximately FL310; and approximately 50 miles NW of ZZZZZ intersection; we notice a slight flicker from the master caution light that immediately extinguished. A few minutes later the light illuminated again. At this point we were able to determine it was the OVHT/DET indication on the recall pad. Indication remained for only a few seconds then extinguished again. All engine indications were normal. A short time later the engine fire warning system illuminated along with the fire warning bell. The number one engine light was illuminated. This indication only lasted for about 2 seconds then extinguished. Again; all engine indications appeared normal. I directed the First Officer to fly the airplane and communicated with ATC while I reviewed the engine fire checklist. At this point however; all indications were normal. Considering all factors; including destination; night time; sporadic and intermittent nature of the warnings; I elected to return to ZZZ after conferring with my First Officer. We elected to accept an overweight landing rather than risk the warning returning during a hold while trying to burn fuel. After reviewing the overweight landing procedure we elected to [request priority handling] and return to ZZZ. Approach and arrival was fully briefed; Flight Attendants were advised of the situation; as well as passengers. I elected to perform the landing as my First Officer was on his second day of IOE. I then took control of the aircraft and landed on Runway XXR. Landing weight was approximately 154;000 lbs; and landing was very soft. After turning off runway we stopped and had crash fire/rescue visually confirm there were no fire indications either with brakes or engines. We then proceed to the gate and deplaned normally. All defects were submitted via ACARS ELB.