Heater blowing clod air

check these sites......

https://www.google.com/search?q=2003+Dodge+Caravan+Grand+Sport+blowing+heat+on+driver+side+vent

Good Luck!

There are two possibilities, one is the thermostat. Many people remove them which spoils the whole heating / cooling system. Since you changed the thermostat, I would check the heater valve on the heater which allows the hot water to circulate through the heating system.
It may be necessary to remove the heater box and flush the heater core since you talk about a lot of rust, which could have clogged the heater core and / or the pipes leading to the heater.

Check engine coolant if it is low it will cause the heat to blow clod. make sure and check it while cold. also if it only last a second or two that is normal the heat controler is in many cases operated by vacuum.

How are your fluid levels? Low coolant flow can cause this. Does the heat go out intermittenly? i.e. when your idle will it go cold and then when you drive away does it get warm again. Could be a few things but, easiest is to make sure your coolant is at proper levels. If that all good try replacing the thermostat.

sound like a faulty thermostat.if thermostat good check HVAC fuse.if all is good problem could be electrical problem to heater air door or faulty or stuck door.the mode switch can also befaulty.

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.

A couple of other things you might want to check are your heater control valve that is controlled by a vacuum line and also make sure you do not have any vacuum leaks in the system.

If the temperature gauge is reading normal, have the heater control valve checked.

misty check the water level in the radiato...if it is low the last thing to get any water is the heater core..if low you will need to find the reason...like a water pump or headgasket leaking

check the coolant level, I had the same problem low coolant level.....no hot water to the the heater coil.