The question has already been covered thoroughly, but I can't help piling on.
Here's how it goes. Heat is conserved due to heat being a form of energy, although temperature is not conserved. (In ordinary English, temperature and heat sometimes mean the same thing, but not in physics.)
So suppose you remove less heat by using slower fans. Then the whole computer temperature will increase (which you don't want) as the quanitity of heat within the case builds up. As the temperature rises, the amount of heat radiated and conducted away from the case gets larger (another law of thermodynamics.) At some elevated temperature the heat leaving the case again matches the amount generated. So you delayed the heat from escaping a few minutes, but ultimately it is just the same. Mostly what will happen is the air coming through the fans will become a lot hotter.
One interesting aspect of temperature not being conserved is that you can decrease the temperature rise that a given amount of heat causes. (For instance higher-humidity air heats up slower.) During the energy crises era, if anybody remembers that, the conservationists often recommended having lots of (sealed) barrels full of water standing around to soak up heat. It takes a lot more heat to raise the temperature of water a given amount compared to air. So you could keep the room cooler by this technique. ( The conservationists idea though was to keep the room warmer when there was no solar engergy available at night.)
The other thing you can do is to dilute the heat by having good air circulation to other parts of the house. Have a room fan on a stand perhaps by the door. In effect, you tranfer control of the heat to the central heating/cooling system.