This is a very common problem on any brand of engine, caused by a failing crankshaft position sensor or camshaft position sensor. They often become heat-sensitive and fail when they get hot, then work again after cooling down for an hour. The more common complaint is the engine runs fine as long as the car is moving and natural air flow keeps the sensors cool, then the engine won't restart after being off for a short time, as in when stopping for gas. "Hot soak" is the term for heat migrating from the stopped engine up to the sensors.
The place to start is by having the diagnostic fault codes read and recorded. The people at many auto parts stores will do that for you for free. Be aware that it can take some time for a fault code to set related to these sensors. The codes often don't set in the short amount of time it takes for a stalled engine to coast to a stop, and they may not set just from cranking the engine. That means don't discount those sensors if there's no fault codes related to them.
Also be aware that fault codes never say to replace a part or that one is bad. They only indicate the circuit or system that needs further diagnosis. When a part is referenced in a fault code, it is actually the cause of that code about half of the time. First we have to rule out wiring and connector terminal problems. In this case, given your description of the symptom, a failing sensor is a better suspect than a wiring problem.
Monday, May 1st, 2017 AT 3:39 PM