CRJ-900 First Officer reported a Landing Gear Overheat Light illuminated after takeoff. After performing the Checklist Procedures did not resolve the issue; The flight crew requested priority handling and performed an air turn back and precautionary landing at departure airport.

Narrative

On DATE; Captain NAME and I operated Aircraft X from ZZZ1 to ZZZ2. Everything was normal until about 2;000 feet when we got the GEAR OVHT Warning. We ran the Emergency Checklist; which had us slow to below 220 knots and lower the landing gear. So we did that while maintaining 5;000 feet. The Brake Temperature Monitoring System started to drop down from 20 to about 14. However; it did continue to spike up to 20; causing the warning to go off; and then go to the yellow dashes to an unknown status. At this point; we could not confirm if we did or did not have a fire; and we deemed it necessary to request priority handling and return to ZZZ1 (Quick Reference Handbook led us to land at nearest suitable airport) where we had fire services and would be the safest for passengers and crew. Upon landing; and applying brakes; the warning went off again. We stopped on the runway; set the brake and communicated with the fire department to inspect for any fire. They found no indication of fire or even overheat. Contract Maintenance came out; deferred the Brake Temperature Monitoring System sensor; and we completed the flight from ZZZ1 to ZZZ2. What caused this issue was a bad Brake Temperature Monitoring System sensor.