An apparatus or a system for an engine, having intake air quantity adjusting means (32, 33) for adjusting an intake air quantity of the engine, ignition means for igniting a fuel supplied to the engine and a catalyst included in an exhaust system of the engine, the apparatus or system comprising control means for controlling the intake air quantity adjusting means (32, 33) and the ignition means, wherein the control means is arranged to: set an ignition timing of the ignition means at or following a compression top dead center time when the engine is operating in an idle state and a request is made to raise a temperature of the catalyst; calculate a target value of the intake air quantity in accordance with an engine request torque; and control the intake air quantity adjusting means (32, 33) so that the intake air quantity becomes the target value; characterized in that the control means is further arranged to: calculate a limit value of the intake air quantity for preventing the exhaust temperature from rising excessively; compare the target intake air quantity with the limit intake air quantity; control the intake air quantity adjusting means (32, 33) so that the intake air quantity becomes the target value when the target value is less than the limit value; and advance the ignition timing based on a difference between the target value and the limit value when the target value is greater than the limit value and while the intake air quantity adjusting means (32, 33) is controlled to set the intake air quantity to become the limit value. set an ignition timing of the ignition means at or following a compression top dead center time when the engine is operating in an idle state and a request is made to raise a temperature of the catalyst; calculate a target value of the intake air quantity in accordance with an engine request torque; and control the intake air quantity adjusting means (32, 33) so that the intake air quantity becomes the target value; characterized in that the control means is further arranged to: calculate a limit value of the intake air quantity for preventing the exhaust temperature from rising excessively; compare the target intake air quantity with the limit intake air quantity; control the intake air quantity adjusting means (32, 33) so that the intake air quantity becomes the target value when the target value is less than the limit value; and advance the ignition timing based on a difference between the target value and the limit value when the target value is greater than the limit value and while the intake air quantity adjusting means (32, 33) is controlled to set the intake air quantity to become the limit value. calculate a limit value of the intake air quantity for preventing the exhaust temperature from rising excessively; compare the target intake air quantity with the limit intake air quantity; control the intake air quantity adjusting means (32, 33) so that the intake air quantity becomes the target value when the target value is less than the limit value; and advance the ignition timing based on a difference between the target value and the limit value when the target value is greater than the limit value and while the intake air quantity adjusting means (32, 33) is controlled to set the intake air quantity to become the limit value.