Air conditioning system for a cabin of an air or rail transport vehicle comprising: - a hot and pressurized air source, referred to as a bleed air source, - a channel for circulating ram air drawn from outside the transport vehicle, - a network of pipes (50, 51, 52, 53, 54, 55, 56, 57, 58, 59; 70, 71) and control valves (20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34) which are configured to be able to control the flow of air circulating through said pipes on the basis of the conditions of use of the transport vehicle, - an air cycle turbine engine comprising at least one compressor and a turbine, referred to as a power turbine, which are mechanically connected to one another, said compressor comprising an air inlet which is fluidically connected to an opening for drawing in outside air and an air outlet which is suitable for being able to be fluidically connected by said pipe network, upon control of at least one control valve, to said cabin in order to be able to supply it with air at a controlled pressure and temperature, and said power turbine comprising an air inlet which is suitable for being able to be fluidically connected by said pipe network, upon control of at least one control valve, to said bleed air source and an air outlet, - at least one heat exchanger, referred to as a primary cooling exchanger, which is accommodated in said ram-air circulation channel and comprises a primary circuit which is supplied with the flow of air from said compressor in thermal interaction with a secondary circuit supplied with said ram air, the system being characterized by: - at least one second heat exchanger, referred to as the main cooling exchanger, which is arranged in said ram-air circulation channel, and comprising a primary circuit supplied with said flow of air from said primary circuit of said primary exchanger in thermal interaction with a secondary circuit supplied with said ram air, and by said pipe network comprising furthermore: - a pipe, referred to as a thermal power pipe, which is suitable for being able to fluidically connect, upon control of at least one control valve (25, 21), said air outlet of said power turbine and said ram-air circulation channel upstream of said primary exchanger such that said bleed air expanded by said power turbine can form a thermal energy source for said ram air being supplied to said primary circuit of said primary exchanger. - a bypass pipe which is suitable for being able to fluidically connect, upon control of at least one control valve, the outlet of the primary circuit of said primary cooling exchanger and the pipe network downstream of said main cooling exchanger, so as to bypass said main cooling exchanger. - a hot and pressurized air source, referred to as a bleed air source, - a channel for circulating ram air drawn from outside the transport vehicle, - a network of pipes (50, 51, 52, 53, 54, 55, 56, 57, 58, 59; 70, 71) and control valves (20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34) which are configured to be able to control the flow of air circulating through said pipes on the basis of the conditions of use of the transport vehicle, - an air cycle turbine engine comprising at least one compressor and a turbine, referred to as a power turbine, which are mechanically connected to one another, said compressor comprising an air inlet which is fluidically connected to an opening for drawing in outside air and an air outlet which is suitable for being able to be fluidically connected by said pipe network, upon control of at least one control valve, to said cabin in order to be able to supply it with air at a controlled pressure and temperature, and said power turbine comprising an air inlet which is suitable for being able to be fluidically connected by said pipe network, upon control of at least one control valve, to said bleed air source and an air outlet, - at least one heat exchanger, referred to as a primary cooling exchanger, which is accommodated in said ram-air circulation channel and comprises a primary circuit which is supplied with the flow of air from said compressor in thermal interaction with a secondary circuit supplied with said ram air, the system being characterized by: - at least one second heat exchanger, referred to as the main cooling exchanger, which is arranged in said ram-air circulation channel, and comprising a primary circuit supplied with said flow of air from said primary circuit of said primary exchanger in thermal interaction with a secondary circuit supplied with said ram air, - a pipe, referred to as a thermal power pipe, which is suitable for being able to fluidically connect, upon control of at least one control valve (25, 21), said air outlet of said power turbine and said ram-air circulation channel upstream of said primary exchanger such that said bleed air expanded by said power turbine can form a thermal energy source for said ram air being supplied to said primary circuit of said primary exchanger. - a bypass pipe which is suitable for being able to fluidically connect, upon control of at least one control valve, the outlet of the primary circuit of said primary cooling exchanger and the pipe network downstream of said main cooling exchanger, so as to bypass said main cooling exchanger.