I recently purchased my vehicle and it runs good.

I recently purchased my vehicle and it runs good, however, after driving a short distance and shutting off the vehicle it won't start back up. It cranks but no start. Once the engine cools down it will start right up. Now from my own personal tests the ignition module is good, when the car doesn't start I'm getting a good spark as well as good fuel pressure. A shop told me that my coil was also good. Now my car is throwing a code for the Idle Air Control Valve but I wasn't to sure if that would affect startup. I noticed that no matter what my radiator fan won't come on but it does work because I hooked it up to a power source. My temperature gauge in the dash reads a normal temperature.