If you take a look at 310.16, the 75C column, you will see the F temps as well. If a conductor/breaker is loaded to the maximum current permitted, the conductor/breaker may reach this temperature (possibly 167F). So the conductor/breaker can actually be hot to the touch, well above the ambient temperature surrounding them.
Some breakers as they get older will buzz due to the pitting of the contacts, which also may increase the breaker temp. Depending on the load applied to the breaker in the picture posted, I would say the buzzing is from pitted or loose contacts, and the temp is not creating this problem. There are many variables, but this is my guess.