First Officer reported a #1 Engine Bleed Air Over Temperature EICAS message in flight. The Flight Crew elected to divert and make a precautionary landing.

Narrative

I was Pilot Flying and Captain was Pilot Monitoring. Airplane had Pack 2 MEL'd so we were limited to FL250 and the cabin was full plus a jump seater. Taxiing out to the runway we requested to sit and burn fuel before we took off from Runway XXL as we were takeoff performance limited due to having a slightly longer route and the aircraft being full. After 10 to 15 minutes of burning fuel; we took off normally and climbed normally. We decided to leave the APU supplying the pack as we believed we were going to be overweight by the time we got to ZZZ. Climbing though 16;000 ft. we entered a broken cloud layer; and soon after we entered icing conditions as indicated on the EICAS. We then switched the engine bleeds to supply the pack and the anti-ice systems. About 20-30 seconds after switching to the engine bleeds; a Bleed 1 OVER TEMP message appeared. Around this time; we also detected a burning smell that disappeared when we turned off engine 1 bleed. Captain ran QRH and we decided to descend to 10;000 ft. as we wanted to exit icing conditions and get to a safe altitude if the aircraft were to have pressurization issues. After descending to 10;000 ft. and coordinating with Dispatch over ACARS; we decided to divert to ZZZ1; due to lack of fuel to fly to ZZZ and cabin temperature issues in the rear of the cabin; as confirmed by the Flight Attendant. on two occasions. At this time; we requested priority handling due to determining we would do an overweight landing. After running checklists and the overweight checklist at approximately 44;000 lbs. we landed Runway XYL with no issues and taxied to the gate normally.