DO NOT remove the headliner under any. circumstance. You cannot access the heater core from the headliner The components are only accessible from the top and roof removal is required Easiest way to determine which screws (in the perimeter of the headliner attach the roof, is to remove one. If it's short, it only secures the headliner, if it's long, it passes through the ROPS structure and secures the roof via RivNuts. The roof securing screws will be every other screw. If the first one is short, replace it and go to the next and then skip every other one and tale out all the long ones.
Remove all of them and then get a buddy to help you pull the roof. It's not heavy but it's cumbersome and required 2 people to get it off. I put a ladder on each side and work off the ladders. Once you remove the roof, inspect the sealing gasket on the roof channel. If it's cracked or getting dried out, replace it. Your dealer can order a new one. The replacement gasket comes wit an adhesive backing and too long so you will have to cut it to size after you remove the old one and scrape off the old adhesive from the channel.
I suspect either of 2 things. One, your heater core is loaded with chaff from a leaking gasket or the water valve is faulty. Both are next to each other and cleaning the core will involve removing it by removing the coolant pipes and cleaning it under a stream of water with dish soap.
Observe the operation of the water valve by operating the temperature control. In cold, it should be closed and in hot, completely open and it's 100% mechanical.
I also suspect if your water valve is operating correctly, then the core is loaded with chaff and the ac HX will also be loaded as well and will need cleaned but you cannot remove it without breaking the refrigerant lines but you can take all the screws out of the top cover and lift it far enough to access the ac heat exchanger and you can then soak it down with a soap and water solution (I use Simple Green) and hose it down carefully with a small stream of water. The accumulated gunk will flow out the condensate drains under the tractor. When the soap and rinse water is clear, you've cleaned the ac HX as well.
There are no controls anywhere but under the roof. The heater hoses run up the right side cab pillar, the ac lines up the left pillar.
I clean mine every other year. Once you do it, it's pretty easy, hard part is getting the roof off.
You also need to look at the gasket that seals the filter element to the roof and replace that foam gasket if it looks at all flattened. I use a weatherstrip bulb gasket on mine.
The above only applies to the earlier units with the heat and ac in the roof. The newer models have the works under the seat and require seat removal and panel removal to access them.
Last time I bought a roof gasket (2 years ago) it was 100 bucks at my dealer. Don't try to cheap out with some box store gasket. The OEM gasket is a specific thickness and designed to fit correctly.
It's a preventative maintenance job you will have to do, probably more than once, depending on how long you keep the tractor.