Hot water constant temperature device, control method thereof and gas water heating equipment

The invention discloses a hot water constant temperature device, a control method of the hot water constant temperature device and gas water heating equipment. The hot water constant temperature device comprises a water storage tank, the water storage tank comprises a tank body and a diaphragm arranged in the tank body, the diaphragm divides the interior of the tank body into a first containing cavity and a second containing cavity, a first water through hole, a second water through hole and a third water through hole are formed in the tank body, the first water through hole and the second water through hole are communicated with the first containing cavity, and the third water through hole is communicated with the second containing cavity. The third water through hole is communicated with the second accommodating cavity; the three-way valve comprises a first connector, a second connector and a third connector, and the first water through hole is connected with the second connector; the first end of the first