The invention primarily relates to an air intake module of an internal combustion engine (1) of a motor vehicle comprising at least two stages of air supercharging (15, 15') of said internal combustion engine (1), characterized in that it further comprises: - means (23) ensuring a first heat exchange with the supercharging air via a high-temperature coolant circuit (2) of the internal combustion engine (1) so as to reduce the supercharging air from a temperature greater than or equal to 150 degrees Celsius to a temperature located within a first range of temperature values; - means (24) ensuring a second heat exchange with the supercharging air via a low-temperature coolant circuit (19) so as to reduce the temperature of the supercharging air within a second range of temperature values, and - means (25) ensuring a third heat exchange so as to reduce the temperature of the supercharging air within a third range of temperature values, before its admission into the combustion chambers of the internal combustion engine (1).