The air conditioning device (10) includes a heat exchanger (12) intended to exchange heat with the air circulating in the air conditioning device (10), and an air distribution box (14), extending in a longitudinal direction (X) between a front part (14A) and a rear part (14B), and in a transverse direction between two side parts (14C). The distribution box is fastened to a ceiling (5) of the driving cabin (1), and comprises: in its front part (14A), a front inlet (16) for air coming from the cabin (1), connected upstream from the heat exchanger (12), and in each of its side parts (14C), a respective side outlet (18) for conditioned air, connected downstream from the heat exchanger (12).