If the thermostat isn't opening it won't allow heated coolant to flow into the heater core and yoou car won't have any heat inside. The car isn't overheating (yet) because the pressure will build to a point that it forces the thermostat open for a brief period, but long enough for there to be coolant flow to keep the engine from overheating. Are you seeing the coolant temp gauge move around at all? This happened to my Taurus not long ago. No heat inside, and the gauge would bounce from lower than normal to higher than normal every few minutes while driving. A new thermostat and everything was fine again.
Did I say "heat" enought times in there?
