bad engine\water temp sensor?

I have a 97 Dodge Intrepid, plenty of miles on it... just recently on a cold start or after the car had sat for a couple hours after being ran, and then started again, I went to drive away and the temp guage shot straight to hot, water light came on, then the temp guage went back down to cold, then straight back up to hot... then back down to just above cold. Half the time it registers cold all the time, other times its just below half guage.... i hear no gurgling or bubbling, no steaming or smoking.... but after the car runs for a few minutes, I've been noticing white smoke\steam out of the exhaust pipe while running. It would do this shortly after being started and would last for a good while. the overflow\coolant tank is full to where it needs to be, the fans run constantly on the radiator (hard wired because I think the last owner did it, due to the sensor being crap) Im wondering if I simply have a faulty temp sensor? I drove it today with heater going full blast just for peace of mind... if its hot, its cycling the coolant. But it never bogged down or quit from over heating... but it is very alarming to see a guage go that quickly to hot after a cold start, or even after its been off for a few hours and started again.