Hi
@Leonidas
The air conditioning HVAC condenser (the part with the pipes coming in and out of it in your original image) is fluid cooled. Check the fluid levels of the engine. There’s an HT (high temp) and LT (low temp) circuit in the engine bay. I’d imagine the condenser is on the LT circuit but can’t remember. There’s a procedure for bleeding the system as sometimes you can get air trapped in the HVAC condenser. This was the case when I picked mine up. It bled out over a few hundred miles on its own.
Second to that, get a local automotive HVAC company to put a set of gauges on the system to see what’s happening. If the system is low then a cheap top up by them may be much cheaper than the faff of time and expense of booking into a dealer. If the refrigerant is low should IA pay for the top up, yes. But what’s your convenience worth. (Anecdotally IA has a history of being stingy with the original gas charge at the factory)
As an aside, and I’m not being funny here, have you switched on the AC? Try turning the temperature knob all the way to low, press the auto button and make sure the light is on for the AC button.