Q:

After car runs with temp normal it drops to tempature reading cold

My car temp reads normal but after warming up the tempature drops showing on the gauge engine is cold and the heat in the car gets cool

A:

More than likely your thermostat is stuck in the open position or gets stuck in the open position after the engine warms up.  Your best bet is to have it replaced.  Since you didn't provide any information about what type of car or any other specifics, there is no way I can answer this question further.