Why does car have rough idle it overheated what could be the problem?

If you suspect overheat has caused a problem, you first need to run a compression test. That way you can eliminate some of the problems that are often caused when an engine is overheated. As you're pulling the plugs for the compression test, make sure the plug colors are even, and light to medium grey. Any dark or damaged plugs can indicate other problems. If the compression test indicates that all cylinders have good, even compression and you just have a dark plug, you may have dodged the big expense. Good luck.