Engine is overheating?

Can you please tell me where the thermostat is located and how I test it?

Here are the facts:
1) If I drive above about 35 mph, the van will suddenly "overheat" according to the gauge.
2) However, it is clearly not a faulty gauge, because the heater gives off no hot air at all.
3) Even when running normally the engine heater gives off no heat.
4) NOTE: When it overheats, if I pull over and shut the engine off. And wait like only 1 or 2 minutes. And turn it back on, the temp gauge returns to normal!
5) Again, if I then start driving again and stay below 35 or so mph, and do not go up a hill, the gauge will read normal.

6) I have had thermostats go bad, water pumps go out, hoses break, fan belts break and radiators lose all their anti-freeze. In such cases and the engine overheats. It takes a looong time for the engine to cool back down. With my current problem, it takes just a minute or so?

7) I have replaced the thermostat, and had the system flushed out, but it has not helped.

What say you?

What would make a car overheat when driving in town with the A/C on and then cool down when A/C turned off and accelerate.