The invention refers to a gas fuelled heating unit for a household appliance, such as for instance a cooking or similar appliance. The unit comprises a burner (2), wherein the fuel-gas supply and/or mixing conduit (1), the air conduit (8) and the flue-gas conduit (14) are flexible hoses in view of enabling the unit to be transported and used in any appliance of the above cited kind. In a preferred manner, the unit also comprises first processor means (7) connected to sensor means (5) to process out and monitor the weighed flow rate of the gas and, as a result, to accordingly drive second processor means (12) connected to respective sensor means (10) to process out and monitor the most appropriate weighed air flow rate.