Actually, the filaments do not make most of the heat, which is a common misconception. The tube conducting makes most of the heat- by that I mean the tube conducting as a matter of its class of operation (class A or AB for example), and conducting due to the signal it is amplifying.
If you disconnect the B+ from the tube so that it is merely lit up but not conducting, you will find that most of the heat is gone.
One exception to this is the 6C33-BC power tube, which has a prodigious filament circuit (which overloads the socket that the tube uses and leads to the failure of the socket; the extreme heat that the socket otherwise sees in service contributes to a large degree to that too, so the smaller pins usually fail first).
So other then the 6C33, the filament is about 15-25% of the heat of the tube. The more class AB the circuit is, the larger the proportion of the heat is filament (since class AB circuits run cooler).
If you disconnect the B+ from the tube so that it is merely lit up but not conducting, you will find that most of the heat is gone.
One exception to this is the 6C33-BC power tube, which has a prodigious filament circuit (which overloads the socket that the tube uses and leads to the failure of the socket; the extreme heat that the socket otherwise sees in service contributes to a large degree to that too, so the smaller pins usually fail first).
So other then the 6C33, the filament is about 15-25% of the heat of the tube. The more class AB the circuit is, the larger the proportion of the heat is filament (since class AB circuits run cooler).