NOVELTY - Producing biomethane adapted to supply a natural gas network integrated with a heat supply process, comprises: producing biogas by methanization of organic matter; pretreating biogas; compressing pretreated biogas; separating pretreated biogas by permeation; providing gaseous retentate to produce biomethane; and heating by separating permeate gas by permeation from first stage of separation to produce gaseous retentate enriched in methane and permeate depleted in methane; supplying heat to the boiler; and evacuating the permeate.    USE - The process is useful for producing biomethane adapted to supply a natural gas network integrated with a heat supply process.    ADVANTAGE - The process: utilizes heat and renewable energies from the biogas production process required for digester, thus does not require additional costs for heating the digester equipment; and does not require additional cost for biogas purification, thus the process is beneficial for small producers.    DETAILED DESCRIPTION - Producing biomethane adapted to supply a natural gas network integrated with a heat supply process for heating the biogas, comprises: producing biogas by methanization of organic matter; pretreating the biogas; compressing the pretreated biogas; separating the pretreated biogas by permeation to produce gaseous retentate containing greater than 89%, preferably greater than 96.5% methane and gaseous permeate containing 10-25%, preferably 20% methane; providing gaseous retentate to produce biomethane; and heating the water in gas boiler. The heat supply process comprises separating permeate gas by permeation from the first stage of separation by permeation to produce gaseous retentate enriched in methane with greater than or equal to 25%, preferably 35% and permeate depleted in methane; supplying heat to the boiler with the gaseous retentate; and evacuating the permeate produced by separation by permeation. An INDEPENDENT CLAIM is also included for apparatus for implementing the process as above per se, comprising at least a production unit of biogas comprising a source of organic matter and digester for producing biogas by anaerobic digestion of the organic matter, a pre-purification unit of the produced biogas, a compressor adapted to compress the pre-purified biogas, a first separation module by membrane permeation of pre-purified and compressed biogas adapted to produce the gaseous retentate and the permeate gas, a means of providing gaseous retentate, means to heat the organic material in the digester comprising at least a heating water circuit adapted to heat the digester, a gas boiler adapted to heat water from the heating water circuit, where the means to heat the organic material comprises a second separation module by membrane permeation of permeate gas from the first separation module permeation adapted to produce the methane-enriched gaseous retentate and the permeate depleted in methane, a boiler with heat supply means for gas with the retentate of the second separation module and a permeate discharge means from the second separation unit.