my 1998 cavelier will heat up setting still then when you start driving it it will cool off and blow cold heat.

Cold Heat? LOL I know what you mean. The thermostat is stuck open - replace it.

Yes check the thermostat. Is this driving in the winter time? Is your A/C turned off? Do you have automatic temp control or do you do it manually and where is your setting placed? Try placing cardboard in front of the radiator on a short drive. If the engine stays relatively warmer, it very well will be a sticky thermostat. If you are an inexperienced mechanic you can change it. Drain the radiator fluid first. If it has been several years since changing it, it is a good time to refill with new "good" brand antifreeze. Check the heater hose also, it may need replacing if soft and spongy. Look in the car manual for the location of the thermostat or ask the car parts counter guy where it is. It should be an easy fix, and don't forget to use a new gasket and gasket lube.