Welcome to the forum.
I assume the 3 minutes is the time to prime and start pumping. Could be a very tiny air leak on the suction side causing that. If the pump motor had a shorted winding it would probably smoke. If it running as quiet as normal, before the heating issue, that probably rules out bearings. Besides, if the bearings were putting that much drag on the motor they would burn up quick. That kind of leaves only ventilation. Quite possibly critters have build something in the air passages. You should feel a pretty good air blast out the rear. They usually suck air from the pump end and blow it out the back. Nothing sacred about this direction though. Try pulling the cover where the wires go in and see what you find. Get back to us and we'll work it further.
Al