Process for treating a hydrocarbon-based feedstock containing hydrocarbons with a content of C7 asphaltenes of at least 1% by mass relative to the feedstock, an initial boiling point of at least 340°C, and a final boiling point of at least 600°C, said process comprising the following steps: a) a step of extracting the feedstock using a solvent or a solvent mixture making it possible to obtain, on the one hand, at least one fraction comprising asphalt and solvent or solvent mixture, and, on the other hand, at least one fraction comprising de-asphalted oil and solvent or solvent mixture, b) a step of separating the fraction comprising de-asphalted oil and solvent or solvent mixture obtained from the extraction step a), making it possible to separate the de-asphalted oil from the solvent or solvent mixture introduced into the extraction step a), c) an optional step of injecting a withdrawal flux into the fraction comprising asphalt and solvent or solvent mixture obtained from the extraction step a), d) an optional step of separating the fraction comprising asphalt and solvent or solvent mixture obtained from the extraction step a), optionally as a mixture with the withdrawal flux introduced during the optional step c), making it possible to separate an asphalt fraction alone or as a mixture with a flux for withdrawal of the solvent or solvent mixture introduced into the extraction step a), e) an optional step of injecting a withdrawal flux into the asphalt fraction alone or as a mixture with a withdrawal flux obtained from step d), the process being characterized - in that step c) and/or e) of injecting the withdrawal flux is (are) present when the softening point of the asphalt is greater than 160°C, - and in that said process comprises a step of conditioning the asphalt fraction obtained from steps a) and/or c) and/or d) and/or e), in solid form, performed as successive or simultaneous substeps: - a substep f) during which the asphalt fraction is heated to a temperature of between 120 and 340°C and above the softening point of the asphalt, - a substep g) during which the asphalt separated from the solvent, from the solvent mixture and/or from the flux is cooled to a temperature below the softening point of the asphalt, in which substeps f) and g) are performed in at least two subunits or in a single unit equipped with at least one means that is capable of keeping the asphalt fraction in motion or stirring or grinding it continuously, at least one means of heating and cooling and at least means that are capable of removing the solvent, the solvent mixture and/or the flux of the process, and the asphalt fraction treated in substeps f) and g) has a softening point excluding solvent and excluding flux of greater than 120°C. a) a step of extracting the feedstock using a solvent or a solvent mixture making it possible to obtain, on the one hand, at least one fraction comprising asphalt and solvent or solvent mixture, and, on the other hand, at least one fraction comprising de-asphalted oil and solvent or solvent mixture, b) a step of separating the fraction comprising de-asphalted oil and solvent or solvent mixture obtained from the extraction step a), making it possible to separate the de-asphalted oil from the solvent or solvent mixture introduced into the extraction step a), c) an optional step of injecting a withdrawal flux into the fraction comprising asphalt and solvent or solvent mixture obtained from the extraction step a), d) an optional step of separating the fraction comprising asphalt and solvent or solvent mixture obtained from the extraction step a), optionally as a mixture with the withdrawal flux introduced during the optional step c), making it possible to separate an asphalt fraction alone or as a mixture with a flux for withdrawal of the solvent or solvent mixture introduced into the extraction step a), e) an optional step of injecting a withdrawal flux into the asphalt fraction alone or as a mixture with a withdrawal flux obtained from step d), - in that step c) and/or e) of injecting the withdrawal flux is (are) present when the softening point of the asphalt is greater than 160°C, - and in that said process comprises a step of conditioning the asphalt fraction obtained from steps a) and/or c) and/or d) and/or e), in solid form, performed as successive or simultaneous substeps: - a substep f) during which the asphalt fraction is heated to a temperature of between 120 and 340°C and above the softening point of the asphalt, - a substep g) during which the asphalt separated from the solvent, from the solvent mixture and/or from the flux is cooled to a temperature below the softening point of the asphalt, - a substep f) during which the asphalt fraction is heated to a temperature of between 120 and 340°C and above the softening point of the asphalt, - a substep g) during which the asphalt separated from the solvent, from the solvent mixture and/or from the flux is cooled to a temperature below the softening point of the asphalt, substeps f) and g) are performed in at least two subunits or in a single unit equipped with at least one means that is capable of keeping the asphalt fraction in motion or stirring or grinding it continuously, at least one means of heating and cooling and at least means that are capable of removing the solvent, the solvent mixture and/or the flux of the process, and the asphalt fraction treated in substeps f) and g) has a softening point excluding solvent and excluding flux of greater than 120°C.