Heating settings
 

Sounds like the thermostat may be failing. Have monitored the coolant temperature with an OBD & cell phone app? (torque) That will tell you if it is opening and closing as it should. My 5.0 regulates around 186* but never gets above 203 or less than 170. Others will vary but you should not see extremes if all is working correctly.
There could still be other causes but since the cabin heating system is simply an extension of the engine cooling system I'd start there first.
Note, that thermostats can be sluggish rather than failing open or closed.

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I believe the OP is talking about the AC system and not the water temperature. It sounds like the system may be working as designed but you should have it checked by a dealer diagnostic's system. I believe there are specific codes to the systems function. Mine works similar with quick warm up followed by maintaining steady temp. What I see could be your concern is that when it reaches your temp setting it starts to cool down to maintain that temp. I don't think the system is that accurate so it will keep adjusting to try to meet your setting. I set mine to 70* F and in Auto mode and leave it there.

Ah, I misinterpreted the OP's statement that the air got cold to mean that it hadn't reached final operating temp beforehand.
Yes, the Environmental Control System varies the output temperature in an attempt to maintain the selected setting. It can use both Heat and A/C within minutes of each other doing so.

The climate control in my XK works better than any other car I have ever had. Mine is on Auto and I rarely ever do anything except raise or lower the temperature. I have never had any other car that I have left in auto work so well, including our 5-year-newer Nissan, which I prefer to run in manual.

My BMW is the worst. It has temperature controls plus a thumb wheel. The thumb wheel seems to be coarse adjustment and I guess the temperature control is supposed to be fine adjust, but it flat out doesn't work. And running it in manual is not so simple either. Of course once you figure it out it is workable, but it is the worst system I have ever seen.

I miss read the OP's original post as well. Like 110reef, my xk has no trouble auto regulating temperature. Other than adjusting up/down temp, about the only other thing I do is turn it off with the top down or setting to cabin recirculate when red-neck trucks spew heavy black exhaust.

I have not considered how good or bad the system is as I have a convertible . What I mean is that being I use it for 3 seasons and usually don't drive in the rain or snow it is difficult for me to gauge how well it works. I always keep it in Auto and set at 70* F. Usually I start the car and while in warm up I drop the top. Always driving with the top down doesn't give me a chance to see how well it regulates the temp. On hot days I feel the AC and on cold days the heat along with the seat and steering wheel heaters. That being the case I assume it is working just fine.

I think you are fiddling with it too much. Put it on auto, set the temp to the final temp that you like, and leave it alone. Yes, it will blast hot air as soon as it can in order to warm things up as quickly as it can. That's the way it works.

I run mine on Auto all the time, except in the heat of the summer, where I find it necessary to crank up the fan speed to keep the cabin cool.

My approach is 'Old School'

I never have my climate control on during startup. And do not use heat for the first 3 minutes.

Reason, this is when the car needs the heat more than you do to get up to operating temperature.
Turning the heat on full blast before the car heats up only blows clod air inside and delays the heating process.
Lastly if you run the ac compressor during the time the engine is cold, you are putting stress on it for no reason.

I use the heated seats and steering, till car gets to up temp, then turn the seats and steering heat off and turn the air on.

As bonus my climate control is never confused, it always sees 178degree water as opposed to 0 to 178 jump.

One note on my car's programing the rear defroster comes on in cold weather at start up weather I have the climate control on or off. Naturally I quickly disable it.

Didn't I see someplace that the AC compressor is on continuously and it functions with a valve instead of a clutch on the compressor like old school systems. I don't understand the 178 degree water statement

On the compressor, I am referring to the drag on a cold engine. Maybe our cars dont have this problem?

178 is about the water temperature when I turn the heat on.

Makes sense as hot air rises - pumping it out of the top vents would just heat your roof lining. ;)

Dont know if any of you were Click & Clack the Tappet Brothers fans. God I miss them. Dowe Cheat'em & Howe

This question of when to turn the heat on was a big running debate.

+1.
And I tend to only use the simultaneous floor and windscreen option. I always leave air conditioning to auto. Keeps the cabin nice and dry.