I'm no eletcronics / electrical expert (I'm a mechanical engineer), but my guess is that it could be a sensor or control systems fault. My gen-1 car has climate control like yours, and when I turn the rotary knob clockwise to increase the temperature setpoint, it often doesn't increase the setpoint displayed at all, and I have to turn and turn and turn it.
I suspect that's because the contacts (potentiometer of similar) has got debris in it, at least when pertaining to increasing the set point. I doesn't seem to have anywhere near the same problem turning the setpoint down and by 0.5degC increments either.
Normally my A/C system's setpoint is left at 20.5degC except in the summer (especially on REALLY hot days, i.e. 30degC and more outside) where I would normally raise it to 21-23degC, because most car systems outside of the Middle East are really only deisnged to achieve about 21degC for outside (in the shade) temperatures of up to 30degC - upping the in-car setpoint just takes the pressure off the system a bit, especially as mine is old.
I suspect my car's 'issue' is through a lack of regular use of the temperature dial and debris (dust/dirt etc) getting in through the years. How easy it is to fix that, I dopn't know.
Your car could have similar issues, just with more of the electronics, or it could be a semi-failure of them due to other reasons (which I have no idea at the moment). Annoyingly, electrical type issues are not easy to diagnose, and main dealers (any make) are notorious for taking the easy (for them) and expensive option of wanting just to swap out components (often guessing [badly] and more than once to which) rather than a proper diagnosis, which might mean all that needs doing is for some electrical contacts/PCBs/sensors to be cleaned.
