Russ,
I agree the breaker probably needed to be replaced. And definitely, the initial panel layout was poor. Remember the ambient air (actually the inside of the panel) around any one breaker needs to be below 25C (77F) or you will reduce it's current carrying capability.
My point was, the temperature of the breaker is not a major factor in troubleshooting a circuit. The behavior of the circuit is more important. If the breaker tripped whenever the compressor kicked in, then it was tripping magnetically. If it tripped after a few minutes of running then it was tripping on overload.
Square D QO breakers only have three positions On, Tripped, and Off. You can not tell what kind of event caused a QO breaker to trip.
