An upper mixing region (210) and a lower mixing region (214) are fed with hot air via a radiator (203) and with cold air by way of respective bypass ducts (205, 208). Respective mixing flaps (212, 219) make it possible to adjust the temperature separately in the two mixing regions, from where the treated air is sent into different parts of the passenger compartment of the vehicle. According to the invention, the two bypass ducts (205, 208) pass below the radiator (203) which makes it possible to minimise the length of the path for the hot air between the radiator and the de-icing outlet duct (221) situated at the upper part of the casing (200) of the installation, and consequently to accelerate a de-icing or demisting of the windscreen required urgently for reasons of safety.