A method for the thermal conversion of heteroatom-containing crude oils into low-heteroatom light and/or middle oils, characterized in that - a heteroatom-containing crude oil which is a hydrophobic and/or hydrocarboncontaining liquid and is selected from a group consisting of heteroatom-containing heavy oils, fats, fatty acids, fatty acid compounds, heteroatom-containing heterolipids, tall oils, resin acids and/or mixtures of said substances is fed into a reactor in which a sump phase is maintained at reaction temperature, said sump phase being a heavy oil phase which is liquid and does not evaporate under reaction conditions, and the stabilization of the sump phase is brought about during the start-up of the process by using as starter sump phase the crude oil to be processed and/or a heavy oil which is miscible with the crude oil, characterized in that the sump phase is stabilized, characterized in that its properties and/or the properties of the products evaporated from it and/or the properties of the released products do not change during continuous operation, - the target products in the light and/or medium oil range resulting from a thermal conversion at a reaction temperature between 200°C and 470°C, preferred between 300°C and 440°C, particularly preferred between 350°C and 410°C, evaporate out of the sump phase and are discharged from the reactor via the released gas-vapor phase, said thermal conversion being achieved without the use of either catalysts, hydrogen or carrier gas streams, - the released gas-vapor phase is cooled, the vapor components are condensed and a formed condensate consisting of low-heteroatom light and/or middle oils is separated and discharged, said low-heteroatom light and/or middle oils having a reduced oxygen, sulfur, nitrogen, phosphorus and/or halogen weight content compared to said heteroatom-containing crude oil used, and - the non-condensing gas phase is discharged. - a heteroatom-containing crude oil which is a hydrophobic and/or hydrocarboncontaining liquid and is selected from a group consisting of heteroatom-containing heavy oils, fats, fatty acids, fatty acid compounds, heteroatom-containing heterolipids, tall oils, resin acids and/or mixtures of said substances is fed into a reactor in which a sump phase is maintained at reaction temperature, said sump phase being a heavy oil phase which is liquid and does not evaporate under reaction conditions, and the stabilization of the sump phase is brought about during the start-up of the process by using as starter sump phase the crude oil to be processed and/or a heavy oil which is miscible with the crude oil, characterized in that the sump phase is stabilized, characterized in that its properties and/or the properties of the products evaporated from it and/or the properties of the released products do not change during continuous operation, - the target products in the light and/or medium oil range resulting from a thermal conversion at a reaction temperature between 200°C and 470°C, preferred between 300°C and 440°C, particularly preferred between 350°C and 410°C, evaporate out of the sump phase and are discharged from the reactor via the released gas-vapor phase, said thermal conversion being achieved without the use of either catalysts, hydrogen or carrier gas streams, - the released gas-vapor phase is cooled, the vapor components are condensed and a formed condensate consisting of low-heteroatom light and/or middle oils is separated and discharged, said low-heteroatom light and/or middle oils having a reduced oxygen, sulfur, nitrogen, phosphorus and/or halogen weight content compared to said heteroatom-containing crude oil used, and - the non-condensing gas phase is discharged.