First thing to check is a blown head gasket.
Run the car with the radiator cap opened, most times you can see bubbles.

Check compression on each cylinder.

Check if there is any evident smoke from the exhaust.

Check for any evident leaks.


The smoke that you were told about could be from the fluid hitting a hot component. ie. exhaust.


Also depends how long the engine was overheated for.


Top 2 I'd do is a compression test and the bubble test for head gasket.


If those 2 are ok, you should be in the clear.

Though keep in mind. that the overheating may have worn component(s) and is on its way out.
Might not show now, but it will later on.