CRJ900 diverted to the nearest suitable airport due to BRAKE OVHT and GEAR DISAGREE EICAS messages.

Narrative

During initial climb out; after gear retraction; I noticed for about 2 seconds before the gear and brake temperature indicators went out that the right inboard brake temperature was a yellow box with dashed lines in it. No abnormalities were noted until; after climbing through FL330; we had a master warning 'BRAKE OVHT'. I called for the checklist and also noticed the right inboard brake temperature box was red with 11 or 12 in it. We followed the checklist; which extinguished the 'BRAKE OVHT' master warning and retracted the landing gear. A few seconds later we had another master warning 'GEAR DISAGREE'. We completed the checklist and chose ZZZ as the nearest suitable airport. The first officer sent an ACARS message to dispatch. At the same time I told ATC we needed to get a vector to ZZZ as well as to start a descent. I gave them the souls on board and asked to have the trucks available. At this time I transferred control of the aircraft to the first officer and talked to dispatch and maintenance via radio patch. I also informed the flight attendants of the condition and that we were in route to ZZZ. I completed the descent and approach checklist as we descended. When we were established on the localizer I took control of the aircraft for landing. The landing was uneventful and we taxied to the gate. I believe the event occurred due to a faulty brake temperature sensor on the right inboard brake.