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, 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 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, 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 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).