Why does 1997 Chrysler Cirrus engine simply stop without warning when hot and not restart until it cools for many hours?

could be so many things. is the check engine light on? if yes retreive codes and diagnose. if no you might have a bad distibutor. common with the 2.5 engine. check fuel preasure first before changing dist. when no start is present you will loose spark and fuel . that is ussually distibutor failure.

does it crank over if it does it could be you fuel pump getting hot i had one that did that.