Does the engine ever run cool? Our engines would overheat without the fan on surface streets. When you hit about 40mph or faster, the engine temperature should start going down. This of course will depend on how hot it is outside. Also know that the Cobra's computer will turn the fans on later than it will on the GT, so it will look like the car is running hot. In my experience, driving surface streets (and especially in traffic) the temp will rise up and the fans will turn on now & then to bring the temps down. The temp will never really drop past that point unless you jump on the freeway and drive for a while. This is actually normal.
Have you checked the Cobra's computer to see if it's really getting that hot? There are two temperature sensors on the engine; if one or both are bad, you could get a false reading. Do you have an engine code reader that can read PIDs (engine sensors)? This will tell you if the computer is getting the correct temperature reading. If it's not, the computer will keep trying to heat up the engine and raise engine temps pretty high.