An air conditioning system for an aircraft passenger compartment, the system including: an air supply circuit connecting at least one external air inlet to at least one air distribution outlet which opens into the compartment, an auxiliary power unit mounted in the supply circuit and configured to compress an air stream in the supply circuit, the supply circuit including a heating first branch that connects the auxiliary power unit to the air distribution outlet, and in which a heating mechanism is mounted, a cooling second branch that connects the auxiliary power unit to the air distribution outlet, and a switching mechanism configured to distribute the air stream between the heating first branch and the cooling second branch.