I have a 98 Dodge Intrepid and my heater blows cold air when it is idle. As soon as I start moving, it blows hot air, what could the problem be? I have had the water heater and belts replaced, the thermostat checked...

is this a HVAC question heater and a/C?
cold engines, make only cold air
hot engines make hot air.
for 100 +years. now.

For car running hot and overheating issues, I suggest to you go through this help links.

Click this link below and go through the troubleshooting procedure to take care of the problems: ----

Car runs hot?

http://howtobyme.blogspot.com/2011/11/car-runs-hot-in-traffic.html
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All types of car overheating problems and troubleshooting?

http://technoanswers.blogspot.com/2011/11/all-types-of-car-overheating-problems.html
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Car freeze overnight and started overheating while driving?

http://technoanswers.blogspot.com/2012/01/car-freeze-overnight-and-started.html

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Engine Overheats and heater blowing cold?

http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html

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Car overheats and Air blows hot at idle?
http://howtobyme.blogspot.com/2011/11/car-overheats-and-air-blows-hot-at-idle.html
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overheating?

http://schematicsdiagram.blogspot.com/2011/12/buick-century-overheating.html
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Car engine Overheats and transmission starts slipping?

http://schematicsdiagram.blogspot.com/2011/12/car-engine-overheats-and-transmission.html
----------This details will help.Thanks.

For car running hot and overheating issues, I suggest to you go through this help links. Click this link below and go through the troubleshooting procedure to take care of the problems: ----Car runs hot? http://howtobyme.blogspot.com/2011/11/car-runs-hot-in-traffic.html
-----------All types of car overheating problems and troubleshooting?

http://technoanswers.blogspot.com/2011/11/all-types-of-car-overheating-problems.html
Car freeze overnight and started overheating while driving?http://technoanswers.blogspot.com/2012/01/car-freeze-overnight-and-started.html-----------Engine Overheats and heater blowing cold?

http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html

---------------------------
Car overheats and Air blows hot at idle?
http://howtobyme.blogspot.com/2011/11/car-overheats-and-air-blows-hot-at-idle.html
--------overheating? http://schematicsdiagram.blogspot.com/2011/12/buick-century-overheating.html
----------Car engine Overheats and transmission starts slipping?http://schematicsdiagram.blogspot.com/2011/12/car-engine-overheats-and-transmission.html
----------This details will help.Thanks.

maybe the blend door is not opening .

This sounds like a bad blend door vacuum actuator to me.
If the heater core is hot at idle, but the inside cabin doesn't get hot air, then the blend door is something to look into.

Good luck on this repair.

The Intrepid doesn't have a vacuum line. It uses a electric motor called a "blend door actuator". It's located on the underside of the heater box near the center of the car.

the thermostat is right under where the top radiator hose runs into the motor

Have you checked the coolant level? What you describe is exactly what happens if the coolant level is low. When stopped at idle, hot coolant is not circulating through the heater core, so no heat. As the engine increases in rpm's when you pull away from the light, the water pump is spinning quicker, and some coolant is making it to the heater core. So check the level, and if it is low, keep an eye on it to see if it drops again. That of course indicates a leak somewhere. Get it fixed, as overheating the engine leads to costly repairs and worse case a new engine. Let me know how you make out with this.

your heater isn't shot, but it might be clogged, in car the heater core is what proved heat to you in the car. The core is connected to the cooling system of the engin. over time it becomes clogged by the stuff that is in you coolant. a way to fix this yourself is to take off the two hose that go to it and using a air compressor and some water to blow it out, make sure the air is at a low psi. and then make sure to run water both ways through it. the heater core is just a small radiator. so to much force could break it, start going in the return hose to help get the debre out. Just be careful!

First check the coolant level in the radiator. Check your heater core hoses on the firewall underneath the hood. Let the car come up to temp. and feel the two hoses. If only one of them is getting hot you may have bad heater core or a bad heater control valve.