I have a Dodge Ram van B250 6 cylinder that.

I have a dodge ram van B250 6 cylinder that seems to be having a problem with the thermostat. Would it give me problems in starting if the thermostat was stuck open or stuck closed? It will start in the morning but it dies after only a few minutes running then it wont start again. It seems to have no pressure in the upper radiator hose. Ive got spark for sure as I have replaced the coil pack high tension wire and the pvc vavle is clear. It did heat up the other morning to the point where the thermostat should have opened up but didnt. Can you give me any ideas? It also seemed to have somekind of air flow problem as I gave it gas while idling