Silverluv, we had this happen on our 96 model. under the radiator there are a couple small black plastic relays(the kind you use when putting fog lights on a pickup),one of those was acting up and caused the same symptoms you described.
Yes. Often times by the time I have them tap on electric relay under radiator and or turn manual fuel override on top of fuel pump she fires up and doesn't bother again for the longest time. I replace both them pieces on the last machine a guy was complaining about this. I think the other posibility is droping the fuel charge when tank is less than half full. I sometimes think an electric charge pump would be nice. Not a common enough problem to worry to much about it. Good luck
Yes they will do that when hot. There is an updated fuel shut off unit from Mother Cummins. Should be a warrenty update item. Can't swear to the "warrenty" part but it should be! Be careful when removing the socket head screws. Good luck. Great engine.