Abstract: The method is intended for heating water used in an appliance connected into a domestic water circuit comprising a feed branch for continuously feeding hot water to said appliance and a discharge branch for discharging the water from the appliance; it comprises a first stage in which a first quantity of heat withdrawn from the water passing through a first portion of said discharge branch is transferred to the water passing through a first portion of said feed branch, said first stage being carried out by means of a first heat exchanger traversed by the water of said feed and discharge branches, and a second stage in which a second quantity of heat given up by a fluid traversing the condenser of a heat pump is transferred to the water passing through a second portion of said feed branch which is downstream of said first portion, said second stage being carried out by means of a second heat exchanger traversed by the water of said feed branch and by said fluid, said second quantity of heat being partly supplie