Hello Les, nice looking unit you have there. That transformer might have gotten hot at some point. I would suggest if the capacitors in the metal cans are original, it may be time to replace them. If there is a short circuit in one of them, excess current could cause overheating.
But because these are output transformers, a possible cause of overheating may have been speaker leads shorted together. Run the amp on the bench and measure the temperatures of both output transformers with a laser thermometer. If they are equal and remain so for more than an hour, say a couple of hours, good chance there was no permanent damage done.
Use the laser thermometer to check resistors, coils and transformers, very handy and prevents burnt fingers too.
Thanks for your contributions to running this valuable site.
John

Sounds good, Les, and that’s a pun.
Something I’ll add for future readers of these forums, is that a tube amp should always work into a load. You must always have a speaker or dummy load connected to the secondary winding of the output transformer. If not, it may self destruct.
Could be what happened here, almost.

This rule contrasts with transistor amp outputs. A power transistor simply doesn’t pass any current when a speaker wire comes loose, so you can power up a transistor amp or radio without the speakers and nothing bad will happen. “The vacuum tube is a voltage device, while the transistor is a current device.” Jn