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 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 (P) in the supply duct read by the pressure sensor . 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 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 (P) in the supply duct read by the pressure sensor . 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 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 (P) in the supply duct read by the pressure sensor . <EOS>