In cold weather, the engine temp goes up to half, but heater still blows cold air. Takes awhile for heat to come on. After the heat comes on, every time I come to a stop, thr ait turns to cold until I accelerate again.

Try to back wash the heater core first if it doesnt work then its clogged up try to turn the heater on the front with the heater off for the back keep an eye on the temp guage if it goes up than normal then its clogged....

Fyi u have to run the engine for awhile with the heater fan on

Check the coolant level in the radiator. If the coolant gets low enough the heater is the first thing to stop working. If there is plenty of coolant and the temp gauge is get in up to the half way mark than it's possible the heater core is just about plugged up. Your local repair shop should be familiar with flushing the heater core. I have had many successful heater core flushes over the years and it can save you thousands. If the heater core is successfully flushed it may not be a bad idea to have the coolant flushed at the same time.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

DO YOU HAVE A CHECK ENGINE LIGHT ON

los of coolant/bad heater contol

Your temp sensor has nothing to do with your heater. The temp sensor needs coolant in order to work properly. So first check the coolant level because if it is low your heater will act the way you describe. Once the coolant gets low enough the heater will blow cold. Another possibility is the radiator cap. After the engine has warmed up it expands when it cools down it contracts. As it is contracting if the cap is weak air can be drawn into the system and cause air pockets to form and will cause the same problem

Could be air in the cooling system , try an bleed the system . On top of the thermostat housing is a bleeder valve , with the engine up to temp. open valve till coolant comes out . Is the coolant full ? What color is the coolant ? Have see where coolant turns like a muddy color an clogges the heater core an engine coolant passages . Check the heater hoses going into the fire wall ,are they hot ? Does your grand prix have manual or automatic climate control ? Duel zone ! Do you hear a clicking sound behind the instrument panel ? Bad temp blend auctuator .

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These details will help.
Thanks.

Heater control valve malfunction will not cause engine to overheat unless coolant is leaking externally...Overheating going down the road can be the result of a few different things...Partly clogged radiator...Insufficient air flow due to possible fan problem...External coolant leak...Make sure fans are operting properly and have cooling system pressure tested for leaks...Gaining and losing heat on the inside of the vehicle usually means system is low on coolant but you must find out where coolant is going

It sounds like you have a blocked heater core ( Small radiator that the interior fan blows through to create the heat inside the car), If you can get access to the heater core pipes you might be able to flush it out but usually they need replacing.
hope this help

Is your heater blowing cold air even after thirty minutes? If it is blowing warm air you might suspect a faulty temp sending unit. I hope this might help you!