There is a second less obvious source of heat aside from the filament heater.
Electrons evaporating from the cathode are accelerated by the voltage difference between the cathode and the anode. The accelerated electrons strike the anode and this generates heat on the anode plates. The heat generated by this process is calculated from the equation:
P = V x I, where V is the voltage across the anode and the cathode and I is the anode current.
It is the same power dissipation equation that applies to transistors.
Sa cathode ray tube (CRT). the energy is given of as light instead of heat.