Heater/Temp. Gauge Problem

I have been having problems with the heater on my 99 Taurus. I was having only cool air blow when using heat on any setting. I replaced the heater core about 2 years ago when same problem happened, but this time I was able to flush the core with a water hose and clear the small clog. Now the heat blows great, but only when the car is moving. When stopped in my driveway it goes back to blowing lukewarm air. Now I also noticed that the temperature gauge on the dash tends to drop to Cold when accelerating from a stop. Otherwise the temp gauge stays at normal operating temp. Anybody have any advice?