In a cooling system used in cooling of a heater housing box, the present invention presents an apparatus for stabilizing power supply of heater housing box cooling apparatus capable of changing over a plurality of taps provided in the winding of a power transformer before the output voltage exceeds an allowable voltage range when turning on alternating-current power supply. For this purpose, first resistor 1 for elevating slowly the output voltage of the power transformer when turning on the alternating-current power supply is provided at the secondary side of the power transformer, direct-current voltage V1 rectified and smoothed from the output voltage is delayed by the charging time of a first capacitor, and an electronic controller for operating a tap changeover relay for automatically changing over the plurality of taps provided in the power transformer is started before the output voltage exceeds the allowable voltage range.