Heating, ventilation and/or air - conditioning installation having: - a main air - conditioning thermodynamic loop (10; 10') for the circulation of a refrigerant fluid comprising, at least, a compressor, a condenser, an expansion member (13; 13') and an evaporator, - a cold-storage heat exchanger (21; 18) able to store cold during operation of the compressor, - a secondary air - conditioning thermodynamic loop (20a; 20'a) incorporating the cold storage heat exchanger (21; 18), the secondary air - conditioning thermodynamic loop (20a; 20'a) being intended to cool the evaporator when the compressor is not operating, the secondary air - conditioning thermodynamic loop (20a; 20'a) comprising a fluid circulation leg arranged in parallel with a section common to the main air - conditioning thermodynamic loop (10; 10') including at least the evaporator, the fluid circulation leg comprising a cold-producing element (21; 23') able to cool the refrigerant fluid intended for the evaporator, the secondary air - conditioning thermodynamic loop (20a; 20'a) comprising a switchover device (16, 22) connected to the storage heat exchanger (21, 18) by two circulation legs arranged in parallel, the installation further comprising one of the following two alternatives: - in a first embodiment, the cold-producing element consists of the cold storage heat exchanger and the switchover device has at least a first position in which the switchover device allows the refrigerant to pass through an expansion device positioned upstream of the cold storage heat exchanger and prevents the refrigerant fluid from passing into a bypass leg that bypasses the expansion device, and a second position in which the switchover device prevents the refrigerant fluid from passing through the expansion device and allows the refrigerant fluid to pass into the bypass leg bypassing the expansion device, the secondary air - conditioning thermodynamic loop then comprising a circulation pump for circulating the refrigerant fluid, or - in a second embodiment, the cold-producing element consists of a secondary expansion device, the secondary air - conditioning thermodynamic loop (20'a) comprises a secondary compressor, and the switchover device has at least a first position in which the switchover device allows the refrigerant fluid to pass through the secondary compressor positioned upstream of the cold storage heat exchanger and prevents the refrigerant fluid from passing into a bypass leg bypassing the secondary compressor, and a second position in which the switchover device prevents the refrigerant fluid from passing through the secondary compressor and allows the refrigerant fluid to pass into the bypass leg bypassing the secondary compressor, the cold storage heat exchanger being able to act as a condenser in the secondary air - conditioning thermodynamic loop (20'a) when the switchover device is in its first position, the refrigerant fluid then being expanded and cooled by the secondary expansion device before entering the evaporator. - a main air - conditioning thermodynamic loop (10; 10') for the circulation of a refrigerant fluid comprising, at least, a compressor, a condenser, an expansion member (13; 13') and an evaporator, - a cold-storage heat exchanger (21; 18) able to store cold during operation of the compressor, - a secondary air - conditioning thermodynamic loop (20a; 20'a) incorporating the cold storage heat exchanger (21; 18), the secondary air - conditioning thermodynamic loop (20a; 20'a) being intended to cool the evaporator when the compressor is not operating, - in a first embodiment, the cold-producing element consists of the cold storage heat exchanger and the switchover device has at least a first position in which the switchover device allows the refrigerant to pass through an expansion device positioned upstream of the cold storage heat exchanger and prevents the refrigerant fluid from passing into a bypass leg that bypasses the expansion device, and a second position in which the switchover device prevents the refrigerant fluid from passing through the expansion device and allows the refrigerant fluid to pass into the bypass leg bypassing the expansion device, the secondary air - conditioning thermodynamic loop then comprising a circulation pump for circulating the refrigerant fluid, or - in a second embodiment, the cold-producing element consists of a secondary expansion device, the secondary air - conditioning thermodynamic loop (20'a) comprises a secondary compressor, and the switchover device has at least a first position in which the switchover device allows the refrigerant fluid to pass through the secondary compressor positioned upstream of the cold storage heat exchanger and prevents the refrigerant fluid from passing into a bypass leg bypassing the secondary compressor, and a second position in which the switchover device prevents the refrigerant fluid from passing through the secondary compressor and allows the refrigerant fluid to pass into the bypass leg bypassing the secondary compressor, the cold storage heat exchanger being able to act as a condenser in the secondary air - conditioning thermodynamic loop (20'a) when the switchover device is in its first position, the refrigerant fluid then being expanded and cooled by the secondary expansion device before entering the evaporator.