Why would my heater blow out cool air when sitting still and then hot air when going down the road and then it's not all that hot

You need to have the heater core flushed or possibly replaced as these cars had a problem with the heater core plugging

sounds like a possible plugged heater core, restricting the flow of coolant. those require a special tool to remove, quick disconnect, just remove both hose from the heater core and back flush the heater core with a garden hose, NOTICE DO NOT DO THIS WHILE HOT IT WILL BURN YOU, this can make a mess, flush it both ways untill it flows clean and with even pressure, then refill the coolant and road test the vehicle to see if is changed.

To troubleshoot this types of problem,click the link below :----http://howtobyme.blogspot.in/2012/02/heater-blows-only-from-defrost.html
--------Go through the procedure to confirm the issue.

------
Engine Overheats and heater blowing cold?

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

---------
Heat blows cold on drivers side and hot on passenger side?

http://schematicsdiagram.blogspot.com/2011/12/heat-blows-cold-on-drivers-side-and-hot.html

-----------

This will help.Thanks.

sounds like a restricted heater core. if you remove the heater hoses from the engine, pour some cooling system cleaner in. let it sit for 10 or 20 minutes, then you can flush with a garden hose.

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

You likely have a restriction in the heater coolant hose circuit - perhaps a coolant control valve not fully opening, or a kinked hose.
Insufficient coolant volume is flowing to keep the heater core hot.
Try back flushing the heater core system with a garden hose to check flow.

First you have to identify what causes the problem.
To do this you have to:
1) When engine is cold check the level of coolant. If it is low fill it up.
2) Start engine and check if engine reaches regular temperature. If your engine is not heated enough it means your thermostat does not work properly and should be replaced.
3) If engine temperature is normal, then check the temperature of pipes that go to/from heater core. These pipes are located up the fire wall (easier access is from the passenger side). If pipe/pipes are cold (even engine is worm) it means you heater core is plugged and should be flushed. Keep in mind, flushing the whole cooling system is different from flushing heater core.
4) If pipe/pipes are hot/warm, turn off the fan, switch controller to the hot position, wait for 3-4 minutes and turn on the fan. Note if the cold air blows first or warm air blows first but it cools down in 5-10 seconds. If the air blows cold than it is most probably the problem with blend door or blend door actuator.
5) If air blows warm first and then cools down, then while running engine and remaining the transmission in PARKING position, press on the gas pedal until your engine reaches 3,000 RPM. Check if your heater blows warm/hot air. If it does, then your water pump does not work properly and should be replaced. If the air still cold, I would suggest to flush the heater core.

It is most probably the problem with blend door or blend door actuator. But just in case I would suggest to follow the entire procedure:

First you have to identify what causes the problem.
To do this you have to:
1) When engine is cold check the level of coolant. If it is low fill it up.
2) Start engine and check if engine reaches regular temperature. If your engine is not heated enough it means your thermostat does not work properly and should be replaced
3) If engine temperature is normal, then check the temperature of pipes that go to/from heater core. These pipes are located up the fire wall (easier access is from the passenger side). If pipe/pipes are cold (even engine is warm) it means you heater core is plugged and should be flushed. Keep in mind, flushing the whole cooling system is different from flushing heater core.
4) If pipe/pipes are hot/warm, turn off the fan, switch controller to the hot position, wait for 3-4 minutes and turn on the fan. Note if the cold air blows first or warm air blows first but it cools down in 5-10 seconds. If the air blows cold than it is most probably the problem with blend door or blend door actuator.
5) If air blows warm first and then cools down, then while running engine and remaining the transmission in PARKING position, press on the gas pedal until your engine reaches 3,000 RPM. Check if your heater blows warm/hot air. If it does, then your water pump does not work properly and should be replaced. If the air still cold, I would suggest flushing the heater core.

First you have to identify what causes the problem.
To do this you have to:
1) When engine is cold check the level of coolant. If it is low fill it up.
2) Start engine and check if engine reaches regular temperature. If your engine is not heated enough it means your thermostat does not work properly and should be replaced.
3) If engine temperature is normal, then check the temperature of pipes that go to/from heater core. These pipes are located up the fire wall (easier access is from the passenger side). If pipe/pipes are cold (even engine is warm) it means you heater core is plugged and should be flushed. Keep in mind, flushing the whole cooling system is different from flushing heater core.
4) If pipe/pipes are hot/warm, turn off the fan, switch controller to the hot position, wait for 3-4 minutes and turn on the fan. Note if the cold air blows first or warm air blows first but it cools down in 5-10 seconds. If the air blows cold than it is most probably the problem with blend door or blend door actuator.
5) If air blows warm first and then cools down, then while running engine and remaining the transmission in PARKING position, press on the gas pedal until your engine reaches 3,000 RPM. Check if your heater blows warm/hot air. If it does, then your water pump does not work properly and should be replaced. If the air still cold, I would suggest flushing the heater core.

did you mount the thermostat properly... sounds like it is reversed

here is a picture of the proper orientation