An engine starting apparatus is equipped with a starter which, when it is required to start an engine, moves a pinion to establish engagement with a ring gear coupled to the engine and energizes an electric motor to produce and transmit torque to the ring gear through the pinion for cranking the engine. When the rate of decrease in current flowing in the electric motor or the rate of rise in voltage appearing at a terminal of the starter or a power supply for the electric motor exceeds a given value after the engine starts being cranked, the engine starting apparatus works as a firing-up determiner to determine that the engine has been fully fired up.

A remote start signal is received wirelessly from outside a motor vehicle and, upon receiving the remote start signal, an internal combustion engine in the vehicle is started and a first device group is activated, including at least one device designed to prepare driving off with the motor vehicle, thus setting the motor vehicle to a remote start state. A control unit of the motor vehicle is designed to determine whether, in the remote start state and before driving off, a person is carrying out a predetermined operating action in or on the motor vehicle that is unsuitable for driving off and, if necessary, to switch the motor vehicle to an ignition ON state in which the internal combustion engine is switched off and a second device group consisting of at least one comfort device is switched ready for operation.