Got a suspicion your amp has some kind of overheating protection, probably more to prevent fires than anything else, but it may also be a self-protection circuit that kicks in above certain temps.
Pretty cheap and simple to build in a circuit that'll sense temp and kick in a relay at a critical temp to cut off power to the transformer(s).
Power light lets you know it's still getting current even though the transformer(s) are cut out since they and the tubes generate the most heat. And tubes do degrade over time from heat.
Everything does actually, just that solid-state stuff ("Transistors") can generally handle higher temps for longer periods.
If all was fine this morning you're probably ok but you might want to check your owner's manual to verify that's what's going on, it should make a note that it has "thermal overload" protection, somewhere.