How hot is too hot?

Yeah, they can get roasty-toasty. High-voltage step-up power transformers are inherently less efficient than their low-voltage cousins, and the circuits they run are also less efficient, meaning that they draw more constant power from the transformer, and also heat up the environment in which the transformer operates. Gives everything that "classic" smell.

I've heard from a couple of sources that "back in the day", a common way to figure out how much money could be saved in the power transformer was to build a few prototypes and get them running under actual conditions . . . then start removing laminations until the transformer got as hot as possible and still be "within spec" for the temperature rise!

Ampx61 - I wonder if power filter cap replacements can have something to do with temperature increase.

Transformer with rectifier and filtering capacitors works much harder than the same transformer (and the same power delivered) on resistive load. Current is drawn in very short pulses of very large amplitude limited only by ESR of caps and transformer's internal impedance. High frequency content of these pulses is heating up the core while larger rms current is heating up the copper (rms value is much higher than average value for narrow pulses).

It might be possible that with older caps (that were a little dry) ESR was higher and amplitude of current pulses was lower (and a little longer) heating less copper and the core. Temperatures of transformer in order of 70 deg C are not unusual and can be even higher if better (higher temp) magnet wire is used. I'm not sure where Curie point is but suspect that much higher than that.

I would seriously question the integrity of the amplifier if the case temperature was so hot you can't hold your hand on it. If the temp is that hot, the varnish type insulation in the transformer core will degrade.

If your bias current is off by a significant amount, then it would increase the heat loss in the transformer since it is driving more power. However, it isn't likely it can be off so much the transformer will become so hot you can't touch it.

New filter capacitors will not increase heat dissipation in a transformer but old ones that leak will. If all this started when you replaced your caps, you should verify they are not connected backwards, as polarized caps installed backwards will indeed leak significantly. If this is the case, then you should replace the caps - don't just flip them around. You are asking for trouble if you do this.

It is possible if the transformers ran at a high temperature long enough, they could be damaged to the point of requiring a rebuild. High heat is not a good thing, ever, even in vacuum tube equipment. Granted vacuum tubes have cathode heaters but even they have an optimum temperature and excessive heat will destroy them.

Generally speaking, you can't hold your hand on a properly operating vacuum tube, but you can on the transformers. If you can't, something is seriously wrong.