Roger is right, however the likelyhood that you would see a rise in tempreature would only show under great strain. (flat out up a long drag with a lot of weight on Etc) and the removal of heat from the air going in would also have a cooling effect.
The purpose of the cooling system is not just to stop overheating but to control the heat.
An engine cooling system works in the sectors
1) Below temp - This is when starting and waming up, the engine is set to restrict flow to get heat into the engine using a thermostat.
2) Running temp - The engine regulates the heat up and down
3) Over temp - The engine does everything to cool but once its in this sector other problems happen quickly
The thermostat, and viscous coupling do the adjustments for 1,
The design, flow, waterways, size of rad, rad cap pressure, keep it in 2, (if you get my drift).
It should never get into 3
If you see a car with an electric fan you will find the fan is never on all the time, in fact often people think it never comes on, it switches off to get back up to running temp and on to cool down.
So in this case its more likely that an engine wants more heat than to be cooled. The system is designed to keep you in sector 2, too cold is no good as is to hot.
Remember that we are dealing with coolant that under pressure so boils at a higher temptature.
Removing a thermostat (or it sticking open) will keep the engine so cold (in sector 1) that people will moan that the heater does not work. A thermostat sticking closed, or a the system losing pressure (rad cap or a leak) and the temp will shoot up and in the case of a 2.4 thats into sector 3.
In the case of the cooling problems that 2.4's are renowned for, this is because one of the controls has failed (Pressure, Thermostat, Blockage etc) and its been into sector 3 and this has caused other problems (Blown gasket, cracked head). This then add huge amounts to the system that it cannot control and Bang.