It is not your thermostat, if the themostat was stuck open the engine would still heat up eventually, if stuck closed the engine would overheat, and since the tubes going through the firewall to the heater core are getting hot means the coolant is going through the heater core, so the issue is elsewhere.
The problem is most likely with the blend door, why the blend door isn't working is what needs to be determined, it could be a fuse but if the HVAC controls are all working otherwise I doubt it's a fuse, the blend door acutator/servo is my best guess since it's a common issue and usually is accompanied by a clicking sound behind the glovebox where the blend doors are located, the clicking is caused by the actuator's plastic gear slipping where it connects to the blend door's arm, there 3 blend doors (temperature, vent selection, and recirculating air flow) and each has it's own actuator/servo, there's a lower one and another higher up (not sure of the location of the 3rd one), the lower one it is said is the temperature blend door, but you should be able to determine which is the correct one simply by watching the actuator/s while changing the temperature settings and see which one is trying to move, the temperature blend door moves to direct the air either through the AC evaporator or the heater core or somewhere in between depending on the control settings.
If you are not getting anything trying to move on the actuators when changing temperature settings then you are having an issue with the control panel itself.
Here's a link a topic concerning the blends doors and a similar issue as your's, read it all but pay close attention to all the posts by [MENTION=85386]ghs215[/MENTION], he describes how to get to the actuators and remove them and replace them, it's not easy to get at them but can be done with his advice and a little patiences.
http://www.toyota-4runner.org/4th-gen-t4rs/260967-blend-door-actuator.html
If you find that both blend doors seem to be operating/moving correctly you make have an issue with debri getting in passed the cabin air filter (also located behind the glovebox) and clogging/blocking things up, even if the actuator is the cause of your issues I would recommend replacing the cabin air filter if it hasn't been replaced, should be done one a year at the very least or more often if you drive in very dusty conditions.