To provide a dampening water supplying device and a dampening water supplying method, with which the temperature of the dampening water stored in a water cistern can be prevented from elevating.

In the dampening water supplying device 10, which is equipped with the water cistern stored with the dampening water D and a water tank 30 with a cooling device 31 for cooling the dampening water D and which supplies the dampening water D from the water tank 30 to the water cistern 20, this dampening water supplying device is so constituted as to equip with a flow rate measuring part 43, which can at least measure either the inflow of the dampening water D flowing from the water tank 30 into the water cistern 20 or the outflow of the dampening water D flowing from the interior of the water cistern 20 to its exterior, an inflow adjusting part 42, which can adjust the inflow of the dampening water D, and inflow controlling part 41, which keeps the inflow within a pre-set and predetermined range by controlling the inflow adjusting part 42 in response to the output of the flow rate measuring part 43, and an outflow adjusting part 51, which keeps the water-level of the dampening water D in the water cistern 20 within a predetermined range.