Here's why:
We've had a low rattling sound coming from the engine compartment for awhile. It would only happen when you turned the A/C compressor on. I checked it out and it sounded like the bearings in the alternator were wearing out. I've heard the same type of sound in other cars so I planned on taking the alternator out and having it re-built when I change the belt this weekend.
Well, as it turns out, the problem was the fan that's right behind the alternator that was going out. Tonight my wife calls and says "the temp thingy is flashing a red light".
I pass out, visions of a cracked, overheated block dancing in my head, regain conciousness and tell her to get off the road and shut it down asap. I turn around to go pick her up and I learn she had just started the car and was at the end of her office driveway. I'm thinking "it can't be overheating already" so I look in the owner's manual and it says the light can signal overheating or that the fan is out (smart light). Open the engine compartment, start it up, A/C on full blast and the engine compartment fan is just sitting there.
Bearings must have worn out completely and over-worked the fan motor.
One of the front fans is making a noise too so I'm checking it out this weekend (thanks to Pablito and his explanation on how to get to those fans). If it's the bearings I'll see if it can be taken apart and just replace the bearings without having to get a whole new fan.
Open the engine compartment, crank the engine, turn the A/C to full blast and listen to all of the fans to see if they are making any noises. If they are, replace them. Ours was working yesterday and it was getting warm like you are talking about.