Can You Help Me??

I have a 1991 Ford Taurus with only 81,000 miles.  It is a 6 cylinder with a 3.8 liter.   I was having a problem with the fan relay sticking on causing the fan to stay on when engine was shut off and draining the battery.  Replaced the relay and also have just replaced the thermostat.  Driving this morning car was ok for about 4 miles then gauge would run high then come back down to the middle. Kept doing this on way to work- approx. 12 miles.  While this is going on the heat to the heater was not kicking in.  On way home was doing the same thing but hot air started working and then gauge would just run in the center not go up and down.  What could be my new problem.  Water pump or something else.