How do you bleed the air from an 97' M3 E36 coolant system?

Only fill it between the lines, fill the radiator to the top when cold :)

It sounds like you overfilled it. On the tank there is a line (next to it says KALT/COLD) you should fill only to this line when the engine is cold.

I hope you used genuine BMW coolant because the coolant used in that car is relatively unique, so if you filled it with something from your local store, you more than likely put the wrong stuff in. If you really like the car, you should drain the entire system, which I hate to say is kind of a pita.

Just to get your car driveable: Let it cool down. Take the extra coolant out using a turkey baster or whatever else that would serve the purpose. Loosen the bleed screw (on thermostat housing). Turn the key to ON position (not engine on, just to ON position). Turn the heat to full blast. Some coolant should come out of bleed screw, when it now longer has any bubbles, tighten bleed screw. (That's directions from Bentley 3-Series manual)

Check out www.bimmerdiy.com, it has a ton of bmw specific repair articles.

The coolant bottle does not could desire to be complete while that is chilly. The radiatior blows warm water into the bottle while the engine is warm and sucks it returned out while it cools down. Overfilling the bottle does not have injury something although. there is not any way you're starting to be led to your engine to overheat that way. Low oil could reason overheating, so verify that. And take the radiator cap off while the engine is "chilly" and make helpful ithe coolant is okay.

I don't think you are supposed to fill that all the way up. It should have a FULL mark about half way. Put the fluid level back where it was. As far as bleeding air off, I think your car has a bleeder screw next to the fill cap. But I doubt that is your problem. The fluid doesn't have enough room to expand when it's hot.

Check your car for coolant leaks, if its overheating, and loosing coolant, check the top of the radiator for any signs of leak, you might be experiencing the water pump going bad.