A heating device for an exhaust system of an internal combustion engine; the heating device comprises: a tubular body, which contains a combustion chamber ending with an outlet duct configured to engage in an exhaust duct of the exhaust system upstream of a treatment device; a fuel injector, which is coupled to the tubular body in order to inject, into the combustion chamber, fuel to be mixed with air, is passive, namely it lacks actuators that can be electrically controlled to generate a movement, and has a movable shutter, which is pressure-controlled in order to inject fuel only when the fuel pressure inside the injector is greater than a predetermined pressure threshold value; a supply duct, which is designed to connect the injector to a pump, which is configured to supply fuel under pressure; a shut-off solenoid valve, which can be electrically controlled and is arranged along the supply duct between the pump and the passive injector; a control unit configured to electrically control the opening and the closing of the shut-off solenoid valve, thus consequently determining the opening and the closing of the passive injector; and a spark plug coupled to the tubular body so as to trigger the combustion of a mixture of air and fuel; the heating device is characterized in that: the tubular body has at least one inlet opening, which can be connected to a fan in order to receive an air flow; it is provided at least one pressure sensor (25, 26) arranged along the supply duct upstream of the passive injector; and the control unit is configured to diagnose the correct operation of the shut-off solenoid valve and/or of the passive injector depending on a fuel pressure in the supply duct read by the pressure sensor (25, 26). a tubular body, which contains a combustion chamber ending with an outlet duct configured to engage in an exhaust duct of the exhaust system upstream of a treatment device; a fuel injector, which is coupled to the tubular body in order to inject, into the combustion chamber, fuel to be mixed with air, is passive, namely it lacks actuators that can be electrically controlled to generate a movement, and has a movable shutter, which is pressure-controlled in order to inject fuel only when the fuel pressure inside the injector is greater than a predetermined pressure threshold value; a supply duct, which is designed to connect the injector to a pump, which is configured to supply fuel under pressure; a shut-off solenoid valve, which can be electrically controlled and is arranged along the supply duct between the pump and the passive injector; a control unit configured to electrically control the opening and the closing of the shut-off solenoid valve, thus consequently determining the opening and the closing of the passive injector; and a spark plug coupled to the tubular body so as to trigger the combustion of a mixture of air and fuel; the heating device is characterized in that: the tubular body has at least one inlet opening, which can be connected to a fan in order to receive an air flow; it is provided at least one pressure sensor (25, 26) arranged along the supply duct upstream of the passive injector; and the control unit is configured to diagnose the correct operation of the shut-off solenoid valve and/or of the passive injector depending on a fuel pressure in the supply duct read by the pressure sensor (25, 26). the tubular body has at least one inlet opening, which can be connected to a fan in order to receive an air flow; it is provided at least one pressure sensor (25, 26) arranged along the supply duct upstream of the passive injector; and the control unit is configured to diagnose the correct operation of the shut-off solenoid valve and/or of the passive injector depending on a fuel pressure in the supply duct read by the pressure sensor (25, 26).