Got a 05 3.5 se just pick up this weekend. It will crank and run for aroun 15-30 minutes then just shut off. No sputter motor just dies. Won’t start till cools off just spins over like out of fuel. When motor cools off will crank and run fine. Also at idle tries to run hot. Fans come on no coolant leaks

 

Check the Engine Coolant Temperature Sensor (ECTS). There is a test procedure in the Factory Service Manual (FSM). Free to download in my signature.

Report back your findings.