My heater will sometimes work but at other times it just blows out cold air. When I turn it off after blowing cold air,...it might go back to hot. Or it might start out blowing warm air and then go cold.

Blend door stuck.

Replace the thermostat.

I like that you were knowledgeable to check both coolant lines tells me you are getting hot coolant through the heater core next thing to check will be the blend door on the inside of your vehicle. The blend door is a door that switches from cold air duct to heater duct depending on what you are using at the time. If it is stuck on the cold air duct you will not get any heat sometimes these doors are vacuum actuated and sometimes they are electrically actuated most the time you are able to see the movement of the motor from inside if you don't see any movement but you hear it move chances are it is the door blend I hope this helps.

HEATER NOT BLOWING COLD,NO HOT AIR FROM HEATER,A/C BLOWS HOT AIR,A/C NOT BLOWING COLD, COLD AIR FROM HEATER,BLEND DOOR ACUTATOR CLOSED,HVAC UNIT NOT OPERATING,
http://alltypesofpartsreplacing.blogspot.com/2012/12/heater-not-blowing-coldno-hot-air-from.html

For this types of problem,i suggest you to check this help links:----Car heater blowing warm, but not hot air?http://schematicsdiagram.blogspot.com/2011/12/car-heater-blowing-warm-but-not-hot-air.html
---------A/C, heater, defroster fan, not working?http://technoanswers.blogspot.in/2012/02/ac-heater-defroster-fan-not-working.html
--------Heater problem?http://technoanswers.blogspot.in/2012/02/heater-problem-on-isuzu-trooper.html
---------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.

Check the radiator level, if it low the hot coolant will not reach the heater. Second may be the water pump, as it wares the clearance increases and the efficiency goes way down and it cannot pump the coolant unless the engine revs are up.....

it sounds like a bad blend door motor.these are controlled electrically and not with a cable like older vehicles did.

Replace the temp control on this car, it should be electrical control not cables.

With the car warmed up,feel the heater hoses,are they both warm/hot near the firewall in the engine compartment?If they are both warm/hot,then the heater core should have circulation through it and it may be a "blend door" issue in the heater a/c assembly.If they are not warm/hot then the heater core could be dirty and plugged up and needs to be flushed.
If the above does not help,a drain and vacuum of the cooling system and vacuum refill will remove any trapped air.
Sometimes,clamping off the top rad hose and holding the engine rpm at 2000 rpm will force trapped air out of the heater core.(Watch temp gauge when trying this)
Lastly,a NEW thermostat doesn't mean its working correctly.

working on 4 and 5 speed that the resistor that broken cold air you got to move the selector to see the motor that move the trap hot and cold sometime when the motor was not move to the hot side for a long time its jam the motor on the passager side under dash put to hot and gently tap the motor tanks pierre