A system for feeding air to an internal combustion engine of a motor-vehicle, comprising: - a feed duct for feeding air to the engine, - an air compressor for the air fed to the engine, arranged along said feed duct, and driven by a turbine, which is in turn driven by a flow of exhaust gases of the engine, - a heat exchanger arranged along said air feed duct, downstream of the air compressor, to cool a flow of air fed by the air compressor, by means of a coolant that circulates in a cooling circuit of the engine. - an auxiliary evaporator, interposed in the air feed duct downstream of the heat exchanger, to further cool the air flow by means of coolant that circulates in an air conditioning circuit (A/C) of the motor-vehicle. wherein said air conditioning circuit (A/C) of the motor-vehicle comprises: - a coolant compressor, - a condenser, which receives the coolant from the coolant compressor, - a first expansion valve, which receives fluid from said condenser, - a main evaporator, which is traversed by fluid coming from the first expansion valve, for cooling a flow of air directed towards the passenger compartment of the motor-vehicle, the outlet for the coolant of said evaporator being connected to the inlet of the coolant compressor, - the auxiliary evaporator, which constitutes the aforesaid evaporator interposed in the duct for feeding air to the engine, the auxiliary evaporator being connected in parallel with the main evaporator within said air conditioning circuit (A/C), - a second expansion valve interposed between said condenser and the auxiliary evaporator, - an electronic controller configured to control the activation of the coolant compressor, both according to the request for air conditioning of the passenger compartment of the motor-vehicle, and the request for cooling the air fed to the engine, said system being characterized in that: - the system further comprise an inner heat exchanger, within which the flow of coolant that goes from the condenser to the first expansion valve enters into a heat exchange relationship with the flow of fluid that goes from the main evaporator to the coolant compressor, - said inner heat exchanger being connected in such a way that the fluid coming from the condenser through the inner heat exchanger then divides into two lines directed towards the two expansion valves (TXV1, TXV2), while the flows coming out from the two evaporators (E1, E2) converge into a single flow before passing through the inner heat exchanger, and in that said electronic controller is configured to enable activation of said coolant compressor for feeding coolant through the auxiliary evaporator only when the engine load is below a predetermined threshold. - a feed duct for feeding air to the engine, - an air compressor for the air fed to the engine, arranged along said feed duct, and driven by a turbine, which is in turn driven by a flow of exhaust gases of the engine, - a heat exchanger arranged along said air feed duct, downstream of the air compressor, to cool a flow of air fed by the air compressor, by means of a coolant that circulates in a cooling circuit of the engine. - an auxiliary evaporator, interposed in the air feed duct downstream of the heat exchanger, to further cool the air flow by means of coolant that circulates in an air conditioning circuit (A/C) of the motor-vehicle. - a coolant compressor, - a condenser, which receives the coolant from the coolant compressor, - a first expansion valve, which receives fluid from said condenser, - a main evaporator, which is traversed by fluid coming from the first expansion valve, for cooling a flow of air directed towards the passenger compartment of the motor-vehicle, the outlet for the coolant of said evaporator being connected to the inlet of the coolant compressor, - the auxiliary evaporator, which constitutes the aforesaid evaporator interposed in the duct for feeding air to the engine, the auxiliary evaporator being connected in parallel with the main evaporator within said air conditioning circuit (A/C), - a second expansion valve interposed between said condenser and the auxiliary evaporator, - an electronic controller configured to control the activation of the coolant compressor, both according to the request for air conditioning of the passenger compartment of the motor-vehicle, and the request for cooling the air fed to the engine, - the system further comprise an inner heat exchanger, within which the flow of coolant that goes from the condenser to the first expansion valve enters into a heat exchange relationship with the flow of fluid that goes from the main evaporator to the coolant compressor, - said inner heat exchanger being connected in such a way that the fluid coming from the condenser through the inner heat exchanger then divides into two lines directed towards the two expansion valves (TXV1, TXV2), while the flows coming out from the two evaporators (E1, E2) converge into a single flow before passing through the inner heat exchanger, and