An apparatus for automatically controlling a constant flow by considering heating load, comprising: a supply tube through which warm water is supplied to each household; warm water ducts which are communicated with the supply tube and are branched to each room respectively, and allow the latent heat of the warm water to be heat-exchanged with the corresponding room; water returning pipes which are communicated with the warm water ducts respectively and to which the heat exchanged warm water is returned; a water returning tube to which flows of the water returning pipes are collected and through which the collected flows are discharged outside; temperature adjusting portions which are installed in each room to set desired temperatures for the rooms and measure an indoor temperature of each room; drivers which are installed respectively in the water returning pipes and each of the drivers opens and closes a passage of the corresponding water returning pipe according to an electrical signal; a variable flow valve (200,300,400,500) which is installed in the supply tube or the water returning tube and varies the flow of the supply tube or the water returning tube according to another electrical signal; and a controller which receives the signal from the temperature adjusting portion of each room and controls both the driver of each respective room and the variable flow valve (200, 300, 400, 500), wherein the controller stores an optimum flow value for each room determined on the basis of the necessary request heat amount of the corresponding room in consideration of heating load per room, wherein, in response to a signal from the temperature adjusting portion of a room where heating has to be stopped, the controller controls the corresponding driver in order to close the passage of the water returning pipe of the corresponding room, whereby the flow through the variable flow valve (200, 300, 400, 500) is reduced in proportion to the ratio of the stored optimum flow value of the closed room to a summation of the stored optimum flow values of all the rooms. a supply tube through which warm water is supplied to each household; warm water ducts which are communicated with the supply tube and are branched to each room respectively, and allow the latent heat of the warm water to be heat-exchanged with the corresponding room; water returning pipes which are communicated with the warm water ducts respectively and to which the heat exchanged warm water is returned; a water returning tube to which flows of the water returning pipes are collected and through which the collected flows are discharged outside; temperature adjusting portions which are installed in each room to set desired temperatures for the rooms and measure an indoor temperature of each room; drivers which are installed respectively in the water returning pipes and each of the drivers opens and closes a passage of the corresponding water returning pipe according to an electrical signal; a variable flow valve (200,300,400,500) which is installed in the supply tube or the water returning tube and varies the flow of the supply tube or the water returning tube according to another electrical signal; and a controller which receives the signal from the temperature adjusting portion of each room and controls both the driver of each respective room and the variable flow valve (200, 300, 400, 500), wherein the controller stores an optimum flow value for each room determined on the basis of the necessary request heat amount of the corresponding room in consideration of heating load per room, wherein, in response to a signal from the temperature adjusting portion of a room where heating has to be stopped, the controller controls the corresponding driver in order to close the passage of the water returning pipe of the corresponding room, whereby the flow through the variable flow valve (200, 300, 400, 500) is reduced in proportion to the ratio of the stored optimum flow value of the closed room to a summation of the stored optimum flow values of all the rooms.