The copper lugs going into the breaker are great conductors of heat. Chill them & it will affect the internal workings of the breaker. But when you stop & the breaker will quickly go back to working as designed. So it really is not an issue unless you have someone chasing the robot on the field with canned of air.
On a non FRC but related subject, the NEMA thermal motor overloads work on the same principle heating an element. The overload element is actually called a heater. In some styles the element actually melts in a controlled way. Anyway to properly size them for the general case you need to take into account the ambient temperature of the controller relative to the motor & they still need short circuit protection.