from this description it is almost impossible to pinpoint the problem.

first of all, overheating is caused by the thermostat only when it is stuck closed, not open. I understand if that was a typo.
second, the fact that the engine runs like crap even when cold(when you start) tells me that the overheating is either just a coincidence that happened alongside another problem or that the overheating has caused another problem.

The running at 200 rpms could be most anything from a sensor to moisture in the fuel or bad timing.. and i am not positive, but i have never seen a car that has a temperature shutoff? i know my 1991 teg got really hot, really REALLY hot, and it was still running. now, these motors are hard to start when they are that hot, i know mine was.
( When you said it runs at 200 rpm when started, do you mean when you start it after it cools down or when still somewhat hot?)
If ithe problem is when it is still hot, the running like crap and the overheating are the same problem. have the check engine light code checked, fix whatever it says is wrong(unless it turns out to be something caused by the heat, and not causing the heat)

FIRST FIRST STEP: give us more information, this is just a shot in the dark from your description.(does the engine overheat only when idling, or when the car is not moving, or at highway speed? any details are helpull.)

Step 1: check coolant level, fill if neccessary, fix any leaks if level continues to go down over time. also, check to make sure cooling fans come on when hot.

step 2: replacing the thermostat is not a big job on the integra, it would probably be worth your time to just do this, it way solve your problem.

step 3: find out how to get the check engine codes out of an integra, and be prepared to perform this the if and when the light comes on again. then fix what is not working.

step 4:if the previous steps dont fix it it may be something more serious, like a water pump or who knows what...