1. Turn up heat all the way to override automatic on control panel. Ruling out control panel issues
2. Check if the the heater core pump is running. That pump is located on driver side under brake booster area. Has to 3/4" hoses. You should be able to feel the motor running or put a stethoscope or screw driver on to see if it is running
3. Heater Valve and check valve. Feel if the lines AFTER the pump heat up and to the heater core heat up. If they stay cold the valve most likely stays closed.
4. and VERY COMMON on all of cars of that vintage: FLUSH the heater core. Get a radiator flush set and install a T at the heater core return line. Disconnect heater core input line from pump/check valve. Flush with garden hose. Flush a lot. That fixed it in all of my Jags. Some have to do it every season. However, if that is the case you should do a complete coolant flush.

Please not if it is the heater core, you may still get some little bit of warm air if you keep fan on low or medium. If that is the case that is a good indicator it needs a heater core flush.

Please know there are detailed instructions for all the above posted all over the board. Or get ALLDATADIY access for guidance.
I hope this helps. I just had been through this with a friends S-Type (it was the valve as one side blew cold and one hot) and my own 2000 XJ8. On that one it was the heater core. After flushing it worked like factory new. Notice: I still had some little heat in that case, but only if I put heat all the way up to override auto and keep fan on middle setting. Otherwise I got cold air blowing. That is because the heater core only partially wams up. The temp sensor mounte don the heater core may sense the hot area of the heater core and signal the automatic control that heater core is hot, even though most of it isn't causing it to blow cold air at you trying to match the temp requested, but can never succeed because in fact its blowing even more cold air. And my 1998 (I bought new back then) started doing that about 6 years into it. Same thing. Heater flush. I found some cars had the flush T already installed in the line from previous owners. FYI, you can get a PEAK flush kit at Autozone for like $ 12.00 or around that.

 

I had seen many posts on the forum, I just didn’t know where to start. This is excellent. Thank you for taking the time to help me out here.
Have a fantastic Thanksgiving and holiday season!
Scott

 

You are welcome. Same to you. I am attaching a picture of the flush tee as it is in mine. It was already in the car when I got it. Meaning its not a back flush. Just a flush. A backflush would be letting the water out at that T and blow it in where the valve is by disconnecting the valve clamp. I guess whoever did that on mine did it for easier access. So, I hooked up garden hose on that T . I disconnected hose at the inlet valve (the one you see at the DENSO valve) and opened the fill cap above the thermostat (silver cap with allen key hole). Then I flushed LOTS of water through fast. I also put the hose in where the silver fill cap is and covered it somewhat with hand and rag and blew threw the other direction. I did that thoroughly a few times switching sides. That did the trick.
IMPORTANT: After that I did a complete coolant flush. (engine and radiator). NOTE: There is a drainplug toward back on engine. Nobody ever mentions that. Draining radiator only will not let all the liquid out of engine. I found out the hard way when I realized I was only able to fill about half the coolant in. Total fill is approx. 6ltr. Refilled with factory spec coolant. (currently the PEAK Pink OAT Premix is an equivalent I found after reading endless discussions on the coolant choice). I did that for 2 reasons. 1 I wanted to get all the tap water out and 2 a clogged heater core indicates to me a flush would be in order.
Keep us updated. I am (and everyone else here) is always interested to find out what it was.

Happy Thanksgiving