Does overheating cause your car to jump timing?

Overheating won't cause it to jump time. The "out of the blue overheating" though is likely a bad head gasket, which will let coolant fill a cylinder or two and the engine won't turn over because the coolant doesn't compress. A simple test to see if that is the problem is to remove the spark plugs and see if any are wet or look like they have been steam cleaned. Now use a socket and breaker bar to turn the engine over and see if coolant comes out of any of the plug holes. If it does you have your answer and how you proceed from there would be to remove the cylinder head and inspect the block, head and measure the heights of the pistons in the bores. The last item is to see if the connecting rod(s) are bent from trying to start it. If the rods measure good then send the head out to be tested and surfaced, install new gaskets and put it all back together. If you take it to a shop you may want to call around and get quotes on head gasket replacement on it.