I also got a C in science in high school. So I feel that I am qualified to answer, as my suggestion is probably as likely to help you out as not.
Placing a cozy over your carboy will insulate it. Which means that if you have yeast inside the carboy generating heat, that heat will tend to stay inside (compared to not using a cozy) and building up. So if you want your fermentation to run hot, then this is a good idea.
If you want to cool the beer, then you would need to find a way to wick the heat away by exposing it to something colder. There are some fancy formulas that involve Thermal Mass and Thermal Conductivity and such like that. They involve numbers and physics I think.
