The filament of the tube is intimately associated with the cathode of the tube which it heats. Room temperature isn’t going to affect them much at all so I wouldn’t worry about that. But a fan is a good idea because heat does wear tubes out, and it also shortens the life of electrolytic capacitors (which are used in the power supply).
Now there is an optimal filament voltage- because that is what controls the cathode temperature. But the lifespan of the tube should be considered also. If the filament voltage is slightly lower you’ll get longer life, just like a light bulb. But if its too low, you can damage the cathode. There are a lot of variables here and this is really the sort of thing that is up to the designer. But as far as a fan goes, its a good practice regardless of tube or solid state.
Now there is an optimal filament voltage- because that is what controls the cathode temperature. But the lifespan of the tube should be considered also. If the filament voltage is slightly lower you’ll get longer life, just like a light bulb. But if its too low, you can damage the cathode. There are a lot of variables here and this is really the sort of thing that is up to the designer. But as far as a fan goes, its a good practice regardless of tube or solid state.