Coolant temp sensor for fuel, temp sender for gauge; two totally different parts, and yes, both could be bad. A bad wiring harness will kill an ECT sensor in a heart beat. Don't know why, just know it does it. So, the first question would be...what kind of shape is your wiring harness in? If the ECT sensor is the hot start problem, your plugs will be wet with fuel, and cranking, and cranking, and cranking, would lessen the likelihood of the car starting. A failing pre-pump, however, by cranking, and cranking, and cranking, you most likely eventually build enough fuel pressure. You'll have to pull your plugs to verify which, if either, is correct. Black fuel soaked...too much fuel, white tipped...not enough fuel.

Chris