The engine is supposed to get hot! The thermostat doesn't even open until the coolant is about 180degF (so it doesn't use the radiator until then). There's no way you can hold your hands under the hood and accurately say "oh, it's too hot." Does steam come out of the overflow tank when the gauge goes to the top? Does the radiator cap start spraying coolant?
If you want to know what I think the problem is, it's the gauge. If you don't believe me, think about this:
How long does it take for the engine to get warm enough that the gauge starts to read in the normal range? About 10 minutes? How long until it gets a little bit higher than it's supposed to be? Another 5 minutes? How much longer until the gauge hits the top? Like 30 seconds, right? Does it seem reasonable to you that the engine is suddenly dumping a whole lot more energy into the coolant? Of course not. The gauge is going up too fast.
Still don't believe me? Try the following:
* Get a cooking thermometer
* Get a multimeter
* Suspend your thermostat in a pot of hot water (hang it from a string)
* Heat the water until the thermostat starts to open. The temp should match the temp on the box (you just replaced it, right?).
* Set the multimeter to measure continuity, and attach it to the two leads on the fan switch
* Heat the fan switch until the dmm reports continuity (switch closed). The temp should be a little higher than the thermostat opening temp (I don't have a spec here, but I can look one up later)
* Heat the sending unit and track resistance vs temperature. I'll look up the spec on that later
When you've done all of the above, I expect that you'll find that all of the aforementioned components are working just fine, yet somehow that pesky gauge still indicates "too hot." You can replace it, learn to ignore it, or do what I did (my '88 dx had the same problem). I put a variable resistor inline with the temperature sending unit, and dialed-in the correct reading on the gauge when the engine warmed up. It kept the gauge reading fairly accurately for another year after I started having trouble. Then the gauge finally quit altogether. Currently it will read the right temp until the car is almost warmed up, then it will drop to zero and won't turn on again until the car is cold & re-started.
If you don't feel like dealing with it, you can sell the car to me (for the right price).