When car reaches normal operating temp. It just cuts off it will not restart until engine is cool when engine cools off then it will start then it will run until it gets to the normal operating temperature then it cuts off.
The place to start is by reading the diagnostic fault codes. Many auto parts stores will read those codes for you for free, but it's important to understand the codes never say to replace parts or that they're defective. They only indicate the circuit or system that needs further diagnosis, or they state the unacceptable operating condition that must be diagnosed.