If a breaker (or a fuse) gets hot, it WILL trip – even if there is no over-amp condition.
If you’re confident that the protected circuit isn’t shorting, then I suggest a closer look at the wire connections to the breaker or the breaker itself being at fault. A voltage drop test across the breaker can readily reveal that it’s faulty.
Connect your voltmeter across the breaker while it’s under the load. An ideal voltage reading would be 0 vac. However, 0 vac is rare. Usually even a good breaker will read in the millivolts range. If higher than that, then continue monitoring the voltage while still under the load. Watch it for ten-twenty minutes by taking another reading every so often.
If it’s getting hot and the voltage drop progressively rises to say – 1 volt and then higher, then there’s a resistance in the breaker. It’s getting hotter. Resistance is rising (heat causes resistance), the voltage drop will increase further…and eventually the breaker will trip due to that.
If not the breaker at fault, the could just be a loose wire connection into the breaker. Test for that by moving your test leads to the wires instead of reading the breaker terminals.
Hopefully you know what I mean by “voltage drop” in order to understand what I’m suggesting.