Ah, so you DIDN'T test the CCRM? That makes more sense. As for the overheating, three minutes shouldn't be enough time for the engine to heat up the coolant that much. It took my Cobra clone about 10 minutes (I think) at idle to warm up enough for the fan to come on. It could have been as much as 15 minutes. From what I've read on here, it's more likely that you've got an air bubble in the system that needs to be cleared out. Basically, I believe the 250* is a false reading, and the coolant really isn't hot enough to turn the fan on.
Is your A/C system pressurized and blowing cold? If it's not, turning the A/C to max still won't turn the fan on because the A/C system won't work if there's no refrigerant in the system. Just tested that on my Cobra just now (just replaced the A/C hoses, haven't refilled the system yet). Can anyone else pitch in on this?
The only way I know of to check if your gauge is reading the right temperature is to get a code reader that reads PIDs (engine sensors) and tells you what the computer sees the temperature is. Another way is to measure the resistance on the ECT and the CTS to approximate the temperature. I think Hissin can tell you a bit more.