Well you would have an alternator and power steering issue if it was the belt. You actually have a KK Liberty, and theres a sister section for that, however the same rules apply to whats wrong with yours, vs the KJ. First off, does the engine warm up to the middle of the gauge, where it normally runs? Does it maintain that temp on the highway, or idling, regardless? If yes, then your thermostat is likely not a factor. Even if it doesn't warm up all the way, it would still likely make heat. Heater cores are VERY often overlooked on the Libertys. Normally, if there is a difference in the temperature of the two hoses going to the heater core, it's probably plugged. That's likely what whoever did that said the heater core was ok. Problem is, I have seen the hoses have almost the exact same temp on Libertys, and the heater cores were plugged. I even argued for a few days with another technician on one he was trying to diagnose. He kept saying the customer had unrealistic expectations, and that its cold out(It was 30 degrees out, and the tech was from florida, whats that tell you?). It took him going for a ride in mine for him to understand how it should work. Chances are, yours is plugged. How many miles are on it? How many times has the coolant been changed? Was the correct coolant put in it(better not be green, if so, its wrong). Wrong coolant, not changing the coolant when supposed to, etc will cause them to plug up. To fix it, requires removing the dash, and sucking down the a/c system.