Heating system for heating a vehicle inner space of a vehicle which has an internal combustion engine by means of a heating heat exchanger, comprising - a first thermal circuit which connects the heating heat exchanger to the internal combustion engine and through which a coolant flows, - a bypass line of the first thermal circuit, which bypass line bypasses the internal combustion engine with a bypass valve in order to form a second thermal circuit, - at least one heat source which is arranged in the flow direction of the coolant downstream of the bypass line, and - a first temperature sensor for measuring the coolant temperature at a coolant output (1.1) of the internal combustion engine, characterised in that - a second temperature sensor for measuring the coolant temperature is provided at a coolant input (1.2) of the internal combustion engine, - a third temperature sensor for measuring the coolant temperature in the flow direction of the coolant is provided upstream of the at least one heat source, and - when there is present a first condition in which the first temperature sensor detects at least one predetermined desired flow temperature (T 4, Soll) of the heating heat exchanger, the first thermal circuit is operated only with the internal combustion engine as a heat source, and when this first condition is not present and when there is present a second condition in which during operation of the first thermal circuit the first temperature sensor detects a coolant temperature which is above the one detected by the second temperature sensor, the at least one heat source is operated as an additional heat source or in which, when the second thermal circuit is operated, the first temperature sensor detects a coolant temperature which is above the one detected by the third temperature sensor, the first thermal circuit is operated together with the at least one heat source. - a first thermal circuit which connects the heating heat exchanger to the internal combustion engine and through which a coolant flows, - a bypass line of the first thermal circuit, which bypass line bypasses the internal combustion engine with a bypass valve in order to form a second thermal circuit, - at least one heat source which is arranged in the flow direction of the coolant downstream of the bypass line, and - a first temperature sensor for measuring the coolant temperature at a coolant output (1.1) of the internal combustion engine, characterised in that - a second temperature sensor for measuring the coolant temperature is provided at a coolant input (1.2) of the internal combustion engine, - a third temperature sensor for measuring the coolant temperature in the flow direction of the coolant is provided upstream of the at least one heat source, and - when there is present a first condition in which the first temperature sensor detects at least one predetermined desired flow temperature (T 4, Soll) of the heating heat exchanger, the first thermal circuit is operated only with the internal combustion engine as a heat source, and when this first condition is not present and when there is present a second condition in which during operation of the first thermal circuit the first temperature sensor detects a coolant temperature which is above the one detected by the second temperature sensor, the at least one heat source is operated as an additional heat source or in which, when the second thermal circuit is operated, the first temperature sensor detects a coolant temperature which is above the one detected by the third temperature sensor, the first thermal circuit is operated together with the at least one heat source.