A preheating module adapted to be attached to a gas water heating appliance for preheating cold water within circulation pipelines disposed inside and outside of the gas water heating appliance prior to the use of said appliance supplying hot water; wherein said preheating module comprises: an incoming pipe section adapted for being connected to an inlet pipe of the gas water heating appliance, and a return pipe section communicating with said incoming pipe section; a water pump provided in the incoming pipe section; a first temperature sensor provided in the return pipe section for detecting temperature of water therein; a cold water incoming pipe section communicating with the incoming pipe section ; a flow sensor provided in the cold water incoming pipe section for detecting a water flow therein; a second temperature sensor for detecting temperature of water in said cold water incoming pipe section; and a controller electrically connected with the water pump, the first temperature sensor and the flow sensor and the second temperature sensor; wherein said controller is configured to detect the temperature of water in the return pipe section via the first temperature sensor after a preheating mode being activated, and start an operation of the water pump if the detected temperature of water is lower than a first temperature threshold (T1); and said controller is configured to detect the temperature of water in the cold water incoming pipe section via the second temperature sensor after sensing the water flow in the cold water incoming pipe section via the flow sensor and start the operation of the water pump to increase the water flow if the detected temperature of water exceeds a third temperature threshold (T3). an incoming pipe section adapted for being connected to an inlet pipe of the gas water heating appliance, and a return pipe section communicating with said incoming pipe section; a water pump provided in the incoming pipe section; a first temperature sensor provided in the return pipe section for detecting temperature of water therein; a cold water incoming pipe section communicating with the incoming pipe section ; a flow sensor provided in the cold water incoming pipe section for detecting a water flow therein; a second temperature sensor for detecting temperature of water in said cold water incoming pipe section; and a controller electrically connected with the water pump, the first temperature sensor and the flow sensor and the second temperature sensor; wherein said controller is configured to detect the temperature of water in the return pipe section via the first temperature sensor after a preheating mode being activated, and start an operation of the water pump if the detected temperature of water is lower than a first temperature threshold (T1); and said controller is configured to detect the temperature of water in the cold water incoming pipe section via the second temperature sensor after sensing the water flow in the cold water incoming pipe section via the flow sensor and start the operation of the water pump to increase the water flow if the detected temperature of water exceeds a third temperature threshold (T3). <EOS>