The maximum anode dissipation for the 300B is 36W (RCA sheet). The filament is rated as 5V at 1,2A. This is about the same as that for a KT88, thus the valve should run no hotter than a KT88 - anything more and it is overloaded (working out of spec). I have seen this happening and some clever Jack saying that it is OK, but for such an expensive valve I would certainly not risk premature failing. This is especially true for a directly heated valve.
Thus, Moog, to determine whether it is in fact working within specs measurements would be needed. But the above should give you something relative to work with.
Regarding valve amplifiers in general, they should all really be well ventilated. It must also be kept in mind that maximum dissipation ratings are based on an ambient temperature of 25 deg. C. If this is higher dissipation must be derated. And yes, heat is the enemy of components. Electrolytic capacitors' life is drastically shortened by excessive heat. Hot to the touch, the life is halved or worse. Other capacitors similarly; they can change value when consistently subjected to heat. Again the specs are valid with a reference of 25 deg C. My experience with some designs: the under-chassis temperature is closer to 40 deg.
and don't tell others I said, but I would not bother too much with pious 'running-in specs'. Valves often come pre 'run-in' from the factory - or used to, not sure about anything these days. My view is that any piece of electronic equipment which changes characteristics after more than an hour of operation should have the components examined; I think I have been around that scene for long enough to make that a considered statement. Not to re-start something here that has been discussed before, but it can be shown physiologically that 'accustoming' of hearing has more to do with perceived run-in changes than electronics. Thus don't leave it on overnight to make up a time figure; listen to it!. It will shorten adaptation time.
