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).
