The thermostat should only go in one way. the wrong way it won't fit right and will leave the housing leaking at the gasket.
You haven't said if the engine is really getting hot or not. i.e., the gauge gets it's signal from a temp sender (mounted on the thermostat housing). If the gauge is just mis-representing engine temp due to a bad sensor, well then you have nothing to worry about. But if the engine really is getting too hot, then you need to worry.
Assuming the engine is really getting hot (and that's a big assumption), next time you are at home for a while, start the car and just let it heat up. Have the hood open and watch the gauge. Somewhere around the R in NORM, the cooling fan should start. Certainly by the time the check gauges light is on, a cooling fan should be running. Is it?
If not, that's is what is causing your engine to overheat. Keep an eye as the temp goes up and up, does a fan suddenly come on? Now there is how the temp goes back down.
This fans may not come on when the should due to:
1) fan motor burned out.
2) EEC-IV coolant temp sensor inaccurate or otherwise faulty.
3) IRCM module faulty
4) EEC-IV module faulty.
If the engine isn't really overheating, then it you probably need a new temp sensor for the gauge. (or the gauge could be bad).