Well, any engine will not run good if it is overheating, as more friction will be occurring in it. Get the overheating problem sorted out immediately, before you blow a head gasket, or scuff the pistons or cylinder bores.
If the $4 thermostat is original, don't even think. Replace it without question. Find out where the leak is, and correct as necessary. Fill up the coolant, and warm up the engine. Take an old radiator hose, and shove it into the fan blades to see if you can stop it from rotating. Be careful when you do this! If the fan stops easily, the fan clutch is done. If you see the coolant boiling in your overflow jug, try replacing the rad cap. Good luck!
