Sounds like the climate control is doing it's job properly.
You set a temperature and once that is reached, it will maintain it. So, put in 23 deg. C and it will pump out hot air until it senses that the cabin has reached that temperature. It will then reduce the temp of air coming out of the vents to keep to 23 deg. C.
To test, you could wait until it reduces the temperature coming out of the vents (as you describe) then turn the climate control off by turning the left hand dial fully anti-clockwise. Open all the windows and let the car refill with cold air and then turn the climate control back on and hit Auto again. It should pump out hot air again until it reaches 23 and then cool down again.