the biggest power consumer in a tube amp is usually the heaters for the cathodeThis statement is rarely true- I think the exception used in audio is the 6C33. For most power tubes - like a KT88- the heat made by the cathode is insignificant compared to the heat made by the tube as a result of plate current though it (its class of operation).
As a result, compared to a solid state amp of the amp power and **same class of operation** , tube amps will make marginally more heat.
If you put a tube amp in standby (no B+) even after sitting there all day the tubes won't burn you (the exception being the 6C33). But after being on only a couple of minutes the same tubes will be much hotter if B+ is also applied!
The problem is that if a solid state amp can't bring home the bacon, then it really doesn't matter how much heat it makes. In high end audio, the **sound** produced is the goal.