96 grand cherokee 5.2 v8 strating problems

[tvalks]

Some times it will start fine but usually after it sits overnight and i start it in the morning the rpms will be about 250 lower then usual and when i move and then take my foot off the gas to brake or coast the engine will stop, but after a run it for 15 minutes or so it will run fine the rest of the day. Some people have been telling me the fuel pump and another said that its the coolant temperature sensor because the warning light for it is always flashing on the screen. Could either of those be the cause what do ya'll think?