Correction.
I address TWO things in this thread.
First : Heater Core removal
I installed a NEW HEATER CORE into my car "sprinter" made by Toyota, but wanted to show the world how to do it. I chose a 4runner for that purpose.
Second: For older cars (except Limited models, thanks for pointing this out)
IF your AC is low or having hot air when you select outside air (cold mode), try this:
The hot coolant shut off valve will leak. Even a 97 4runner with 180 K miles will leak (I checked 2 trucks and they both leaked).
I pulled mine out and washed and blow in it while the valve is closed. It is leaking.
If you see the inside of the heater/AC control box, you will see the door DOES NOT close the heater core 100%. So about 20% AC air will pass through the heater core when you have AC or simple outside air on. If hot water comes to the heater core this 20% opening will warm the cold air generated by the AC lowering your AC efficiency.
I practically saw this in my 92 car. I isolated the heater core due to the leak. During hot summer days I simply used speed of 2 or 3 max to cool my car. This is what lead me to this conclusion.
Try it your self, When you are running AC, check the water hose AFTER the valve and the return hose from the heater core, if the hoses are hot like the lower radiator hose, you are sending hot coolant in to kill the cooler air generated by the AC.
I hope this clarify.