Most of you missed the answer completely.
The heat produced by the CPU is entering the room at a given rate that does not change. This raises the temperature of the room until the temperature of the room is greater than the surroundings. When this happens, the room looses heat to the surroundings, unless of course the room is insulated.
If you increase the convection coefficient of the heat transfer between the CPU and the air around it, you lower the temperature of the CPU. You do not decrease the rate at which the room heats up.
Without a high convection coefficient (i.e, no fans), the temperature of the CPU increases until the heat transfer rate equals exactly the heat transfer rate with the fans (until the chip catches fire 🙂 )
So the temperature of the room can't be changed at all based on the convection coefficient, because overall you're not changing the heat transfer rate. Now, you could change the rate of heat transfer to the immediate local surroundings by decreasing the convection and increasing the temperature of the PC case, but thats not changing the uniform temperature of the room.