BMW Repair: overheating at idle, head gasket leak, coolant levels

Question
QUESTION: Hi I own a 1984 BMW 528e and recently my car is over heating.
I have changed the thermostat and the coolant levels are full.
What could be causing this problem?

ANSWER: Possibly waterpump, and possibly head gasket leak.

The head gasket leak can be detected with a "sniffer" that looks for hydrocarbons in the coolant.  Many Firestone stores, and other repair facilities, can do that for ~ $50.

---------- FOLLOW-UP ----------

QUESTION: How do I test the thermostat? Is there a way I really dont
want to spend money on replacing parts that are fine? Is there
a way to tell or is it just a guess?

Answer
You can test the thermostat by putting it in a pot of water with a thermometer in the water.

As the water heats, note the temperature the thermostat opens at.

The odds of a new thermostat being bad are extremely low.  I'd move on to other things.