Car heater intermittently not working

I have a hyundai i30 2009. Starting early last year, the heating has intermittently failed.

When the heating is working, this is what happens:

When the problem occurs, the heating stops working and I get this:

Note that the A/C button is not meant to do anything if the temp dial is set to a value such that air conditioning is not required. The A/C button being on is not meant to prevent the heating from working. This is according to the manual and to my experience.

For the last couple of weeks, I've been testing the heating every time I drive. I drive 2-3 times a day, each drive is about 10-20mins in length. Here are my notes:

• The problem does not correlate to whether i'm accelerating. i.e. it is NOT the case that the problem only happens when I idle.

• The problem does not seem to correlate with the outside temperature.

• The problem does not seem to correlate with how long the car has been sitting still for. i.e. if the engine has fully cooled down from the last drive.

• All vents behave the same. i.e. it's not the case that i'll get hot air from one vent and cold air from another.

• I've tried to turn off the car and restart it a few times when the problem happens. This does not seem to fix the problem.

• When the problem happens, it stick around for a few hours, maybe a day. Then it will just magically go away. I'll start my car and go for a drive and the heating is just magically working again.

Does anyone have any ideas on potential causes or triggers? I'd like to get some ideas before I take it back to the mechanic for my next car service. For my last car service, I was told they could not diagnose the problem because the problem was not happening that day.