A thermal storage air conditioner comprising: a refrigerant circuit including a compressor, an outdoor heat exchanger, an indoor heat exchanger, a liquid refrigerant channel connecting a liquid end of the outdoor heat exchanger and a liquid end of the indoor heat exchanger, a gas refrigerant channel connected to a gas end of the indoor heat exchanger, and a bypass channel having one end connected to the liquid refrigerant channel and the other end connected to the gas refrigerant channel; a thermal storage circuit which is configured to allow a thermal storage medium, which would generate a solid component if cooled, to flow therein; a thermal storage heat exchanger which is connected to the bypass channel and the thermal storage circuit, and configured to allow a refrigerant flowing through the bypass channel and the thermal storage medium flowing through the thermal storage circuit to exchange heat; a refrigerant temperature sensor at an inlet of the thermal storage heat exchanger for detecting the temperature of the refrigerant at the inlet of the thermal storage heat exchanger; a pressure regulating mechanism provided in the bypass channel between the thermal storage heat exchanger and the gas refrigerant channel, and an operation control section, wherein the refrigerant circuit is configured to perform a cooling and cold thermal energy storage cycle in which a discharge end of the compressor is connected to a gas end of the outdoor heat exchanger, a suction end of the compressor is connected to the gas refrigerant channel, the outdoor heat exchanger is configured to serve as a condenser, and the indoor heat exchanger and the thermal storage heat exchanger are configured to serve as evaporators, the pressure regulating mechanism is configured to regulate a pressure of the refrigerant flowing between the thermal storage heat exchanger and the gas refrigerant channel, and the operation control section is configured to instruct the refrigerant circuit to perform the cooling and cold thermal energy storage cycle, and to adjust the amount of pressure reduction by the pressure regulating mechanism during a cooling and cold thermal energy storage operation, in which the cooling and cold thermal energy storage cycle is performed, such that an evaporating temperature of the refrigerant in the thermal storage heat exchanger, detected by the refrigerant temperature sensor, does not fall below a predetermined lower limit evaporating temperature. a refrigerant circuit including a compressor, an outdoor heat exchanger, an indoor heat exchanger, a liquid refrigerant channel connecting a liquid end of the outdoor heat exchanger and a liquid end of the indoor heat exchanger, a gas refrigerant channel connected to a gas end of the indoor heat exchanger, and a bypass channel having one end connected to the liquid refrigerant channel and the other end connected to the gas refrigerant channel; a thermal storage circuit which is configured to allow a thermal storage medium, which would generate a solid component if cooled, to flow therein; a thermal storage heat exchanger which is connected to the bypass channel and the thermal storage circuit, and configured to allow a refrigerant flowing through the bypass channel and the thermal storage medium flowing through the thermal storage circuit to exchange heat; a refrigerant temperature sensor at an inlet of the thermal storage heat exchanger for detecting the temperature of the refrigerant at the inlet of the thermal storage heat exchanger; a pressure regulating mechanism provided in the bypass channel between the thermal storage heat exchanger and the gas refrigerant channel, and an operation control section, wherein the refrigerant circuit is configured to perform a cooling and cold thermal energy storage cycle in which a discharge end of the compressor is connected to a gas end of the outdoor heat exchanger, a suction end of the compressor is connected to the gas refrigerant channel, the outdoor heat exchanger is configured to serve as a condenser, and the indoor heat exchanger and the thermal storage heat exchanger are configured to serve as evaporators, the pressure regulating mechanism is configured to regulate a pressure of the refrigerant flowing between the thermal storage heat exchanger and the gas refrigerant channel, and the operation control section is configured to instruct the refrigerant circuit to perform the cooling and cold thermal energy storage cycle, and to adjust the amount of pressure reduction by the pressure regulating mechanism during a cooling and cold thermal energy storage operation, in which the cooling and cold thermal energy storage cycle is performed, such that an evaporating temperature of the refrigerant in the thermal storage heat exchanger, detected by the refrigerant temperature sensor, does not fall below a predetermined lower limit evaporating temperature.