Heat

Ambient temperature will effect how much heat you amplifier can dissipate. The warmer the ambient temperature the less it will be able to. Airflow will greatly enhance an amplifiers ability to dissipate heat.

I use 12" computer cooling fans on my preamp - on both the power supply unit and the line level unit. I've mounted them in butcher blocks which I have laid flat on top of both the chassis'. The blocks are cut to the same dimensions as the pre-amp chassis' and the fans are orientated to extract air from the pre amp units. Both units are now cool to the touch no matter what the ambient temperature is, where before they were noticeably warm.

I cannot say if it will extend the life of the amp or the tubes, but I'm sure it doesn't hurt. It helps to dampen any chassis vibration and I definitely think the noise floor is a little lower. 

Then if the room is cooler, the heat s being drawn through the heat sinks with greater efficiency?

Yes. Cold air consumes more energy (heat) from the cooling than warmer air can. 

Two factors come into play. 1.) The colder the air, the more heat it can absorb before it reaches a temperature where it will no longer absorb heat from the sinks. 2.)The faster the rate you can replace the air that has already absorbed heat from the sinks with cold (room temperature) air, the faster the rate that heat can be transferred away from your amp.