A continuous flow heating system for heating chemical molecules for organic chemistry reactions and catalysis comprising: - several modules (M 1 , M 2 , ...M N , N ≥ 2), disposed in series, with a module (M i ) comprising: - a circulation tube (TE i ) passing through a waveguide (G i ) configured to heat chemical molecules, and emerging into a temperature-maintaining enclosure (E i ) of the chemical molecules, the waveguide (G i ) comprising a microwave power source (S i ) generating incident power (PIG i ), an isolator (ISO i ) protecting the microwave power source (S i ) from reflected power (PRG i ), directional couplers (CDI i , CDR i ) for measuring incident power (PIG i ) and reflected power (PR), an impedance matching device (ADIMP i ), and a short-circuit (CC i ); - a circulation tube (TS i ) for circulating the products derived from the chemical reaction occurring in the temperature-maintaining enclosure (E i ); - at least one thermal sensor (CT i1 ) for measuring the temperature in the circulation tube (TE i ) between the outlet of the waveguide (G i ) and the inlet into the temperature-maintaining enclosure (E i ); - at least one thermal sensor (CT i2 ) for measuring the temperature in the temperature-maintaining enclosure (E i ); and - at least one thermal sensor (CT i3 ) for measuring the temperature in the circulation tube (TS i ) at the outlet of the temperature-maintaining enclosure (E i ); and - an electronic control unit (UCE) of the system configured to: - control the incident power (PIG i ) of each waveguide (G i ) emitted by each corresponding microwave source (S i ), and the power (PE i ) delivered by each temperature-maintaining enclosure (E i ), as a function of the temperatures measured by the thermal sensors (CT i1 , CT i2 , CT i3 ) and corresponding setpoint temperatures (Tcons i1 , Tcons i2 , Tcons i3 ); and - receive the incident power (PIG i ) and reflected power (PRG i ) measurements intended for setting the impedance matching devices (ADIMP i ) and the short-circuits (CC i ). - several modules (M 1 , M 2 , ...M N , N ≥ 2), disposed in series, with a module (M i ) comprising: - a circulation tube (TE i ) passing through a waveguide (G i ) configured to heat chemical molecules, and emerging into a temperature-maintaining enclosure (E i ) of the chemical molecules, the waveguide (G i ) comprising a microwave power source (S i ) generating incident power (PIG i ), an isolator (ISO i ) protecting the microwave power source (S i ) from reflected power (PRG i ), directional couplers (CDI i , CDR i ) for measuring incident power (PIG i ) and reflected power (PR), an impedance matching device (ADIMP i ), and a short-circuit (CC i ); - a circulation tube (TS i ) for circulating the products derived from the chemical reaction occurring in the temperature-maintaining enclosure (E i ); - at least one thermal sensor (CT i1 ) for measuring the temperature in the circulation tube (TE i ) between the outlet of the waveguide (G i ) and the inlet into the temperature-maintaining enclosure (E i ); - at least one thermal sensor (CT i2 ) for measuring the temperature in the temperature-maintaining enclosure (E i ); and - at least one thermal sensor (CT i3 ) for measuring the temperature in the circulation tube (TS i ) at the outlet of the temperature-maintaining enclosure (E i ); and - an electronic control unit (UCE) of the system configured to: - control the incident power (PIG i ) of each waveguide (G i ) emitted by each corresponding microwave source (S i ), and the power (PE i ) delivered by each temperature-maintaining enclosure (E i ), as a function of the temperatures measured by the thermal sensors (CT i1 , CT i2 , CT i3 ) and corresponding setpoint temperatures (Tcons i1 , Tcons i2 , Tcons i3 ); and - receive the incident power (PIG i ) and reflected power (PRG i ) measurements intended for setting the impedance matching devices (ADIMP i ) and the short-circuits (CC i ). <EOS>