An apparatus (1) for continuous tempering of cacao-butter-containing or other fat-containing, chocolate-like mass flowing therethrough. In the apparatus (1) a predetermined, controlled cooling- or heating-stage of the mass is provided. The apparatus (1) comprises a cooling zone (2) with a plurality of cooling surfaces (3), and a subsequent heating zone (4) with a plurality of heating surfaces (5) for the mass during its passage through at least two sections (C 1 -C n ; H 1 -H n ). The sections comprises mass treatment chambers (6) in succession with associated cooling- or heating medium chambers (7,8). According the invention there is in relation to said sections (C 1 -C n ; H 1 -H n ) of mass treatment chambers (6) arranged at least one heat transmission barrier (9). During operation of the apparatus (1) the heat transmission barrier (9) reduces the heat transmission between the sections (C 1 -C n ; H 1 -H n ) in between which it is arranged to an essentially eliminating and almost imperceptible level. A substantially better controlled tempering process is therefore provided inside a specific section (C 1 -C n ; H 1 -H n ).