As mentioned repeatedly...it is the IHKA temp sensor that regulates the temp that is set on the panel.
BMW changed the design around
7/2012 from the forced air ventilation design (where cabin air is sucked into the IHKA over a sensor/thermistor) to this style that you have that looks like a little button.
Some reasons for the change from the forced air design to the button temp sensor was the complaints over the decades of noise that the little fan would begin to make as dust accumulated and stuck to the little fan inside.
Again...it ACTUALLY IS a temp sensor. But still feel free to ask your local dealership...who may not even know what it is, either.
See
#17 in the illustration below from the BMW TIS...as well as the functional description of the
interior temp sensor...again from the TIS website: