A control system for an internal combustion engine that is installed on a vehicle as a motive power source and is connected, as a motive power source, to a heat supply device that supplies heat to an air conditioner of the vehicle, wherein the air conditioner includes an electric fan, the control system executing idle stop control for temporarily stopping the engine during stoppage of the vehicle and restarting the engine from the temporarily stopped state, comprising: lower limit blowout temperature-setting means for setting a lower limit value of a blowout temperature that is a temperature of air blown out from the air conditioner into a compartment of the vehicle, as a lower limit blowout temperature (TAO_L); estimated blowout temperature-calculating means for calculating an estimated value of the blowout temperature as an estimated blowout temperature (TAO_EST); and control means for causing the engine to be restarted when the estimated blowout temperature (TAO_EST) calculated when the engine is in the temporarily stopped state has become not higher than the lower limit blowout temperature (TAO_L); air conditioner suction temperature-detecting means for detecting a temperature of air sucked into the air conditioner as an air conditioner suction temperature; and power parameter-detecting means for detecting a power parameter indicative of electric power supplied to said electric fan, wherein said estimated blowout temperature-calculating means comprises: stop-time blowout temperature-calculating means for calculating the blowout temperature in timing in which the engine is temporarily stopped, as a stop-time blowout temperature (TAO_STP); temperature drop amount-calculating means for calculating a temperature drop amount (α) of the air blown out from the air conditioner after the timing in which the engine is temporarily stopped, using the air conditioner suction temperature detected when the engine is in the temporarily stopped state, and the power parameter detected when the engine is in the temporarily stopped state, said temperature drop amount (α) representing a value of a drop amount of a compartment temperature per unit time; and subtraction means for calculating the estimated blowout temperature (TAO_EST) by subtracting the product of time period (TOFF) elapsed after the engine is in the temporarily stopped state and the calculated temperature drop amount (α) from the calculated stop-time blowout temperature (TAO_STP). lower limit blowout temperature-setting means for setting a lower limit value of a blowout temperature that is a temperature of air blown out from the air conditioner into a compartment of the vehicle, as a lower limit blowout temperature (TAO_L); estimated blowout temperature-calculating means for calculating an estimated value of the blowout temperature as an estimated blowout temperature (TAO_EST); and control means for causing the engine to be restarted when the estimated blowout temperature (TAO_EST) calculated when the engine is in the temporarily stopped state has become not higher than the lower limit blowout temperature (TAO_L); air conditioner suction temperature-detecting means for detecting a temperature of air sucked into the air conditioner as an air conditioner suction temperature; and power parameter-detecting means for detecting a power parameter indicative of electric power supplied to said electric fan, wherein said estimated blowout temperature-calculating means comprises: stop-time blowout temperature-calculating means for calculating the blowout temperature in timing in which the engine is temporarily stopped, as a stop-time blowout temperature (TAO_STP); temperature drop amount-calculating means for calculating a temperature drop amount (α) of the air blown out from the air conditioner after the timing in which the engine is temporarily stopped, using the air conditioner suction temperature detected when the engine is in the temporarily stopped state, and the power parameter detected when the engine is in the temporarily stopped state, said temperature drop amount (α) representing a value of a drop amount of a compartment temperature per unit time; and subtraction means for calculating the estimated blowout temperature (TAO_EST) by subtracting the product of time period (TOFF) elapsed after the engine is in the temporarily stopped state and the calculated temperature drop amount (α) from the calculated stop-time blowout temperature (TAO_STP). stop-time blowout temperature-calculating means for calculating the blowout temperature in timing in which the engine is temporarily stopped, as a stop-time blowout temperature (TAO_STP); temperature drop amount-calculating means for calculating a temperature drop amount (α) of the air blown out from the air conditioner after the timing in which the engine is temporarily stopped, using the air conditioner suction temperature detected when the engine is in the temporarily stopped state, and the power parameter detected when the engine is in the temporarily stopped state, said temperature drop amount (α) representing a value of a drop amount of a compartment temperature per unit time; and subtraction means for calculating the estimated blowout temperature (TAO_EST) by subtracting the product of time period (TOFF) elapsed after the engine is in the temporarily stopped state and the calculated temperature drop amount (α) from the calculated stop-time blowout temperature (TAO_STP).