CRJ700 Pilot reported BRAKE OVERHEAT MESSAGE in cruise. The flight crew made a precautionary landing at destination airport.

Narrative

While flying straight and level at approximately 20;000 ft. and being airborne for 30 mins. we received a BRAKE OVHT MESSAGE. After running the QRC and the QRH Procedures (pushing the BTMS OVHT RESET BUTTON twice) indications went back to normal. Initial indications showed brake temperature at 15 and red then it started to flicker up and down and eventually stopped at 0 and red flashing indications. We made the standard call to the Flight Attendants and a PA announcement to the passengers advising them that we would be landing in ZZZ with a minor system malfunction and the equipment would be standing by to confirm that the airplane was safe to continue to the gate. We determined that it was the most conservative and safest course of action to [request priority handling] and have crash fire and rescue standing by. After landing the fire trucks took a thermal reading of the right outboard brakes and determined everything was normal. We requested that a truck follow us to the gate as a precautionary measure. After parking and visually inspecting the brakes we determined that everything was normal; thanked the emergency personnel for their help; then contacted Dispatch and Maintenance Control.