When you use a cycle footpump the air gets hotter during use as it compresses. However when you use a fan the air gets colder. Although not being compressed there is still a force on the air molecules. Why the extreme differences between the two?
A fan does not necessarily make the air colder. The air blowing across your skin causes moisture there to evaporate, which makes your skin feel cooler.
The components in the computer are much hotter than the air in the room.
Without a fan the air in the box would heat up and not be able to escape quick enough to stop the components overheating. The air in the box would become hotter and hotter - much as if you left an electric heater on in a closed room.
The fan drives a flow of cooler air from the surrounding room through the box so that heat from the components can be carried away, preventing over-heating
Yes a sort of equalizing or reducing the computer to room temperature then.
The human body is about 37deg C therefore ignoring the effect of skin moisture a fan would do the same to the human body wouldn't it therefore not all in the mind?
"Ignoring the effect of skin moisture", sure, but how can you reasonably ignore it? There IS moisture on the skin, esp. in a hot room, and evaporation is a cooling process. Not all in the mind at all.