The invention relates to a tempering device (1) for objects (2) located on the object carrier (3) of a microtome (4) of a cryostat (5) comprising an operating means supply (6) connected to a cooling device or a cooling and heating device (7) arranged on the object carrier (3), and a temperature control system. According to the invention, one such tempering device (1) is embodied in such a way that the operating means supply (6) does not hinder the work carried out on the microtome (4), and the accuracy of the cut is affected as little as possible. To this end, the operating means supply (6) is displaceably positioned in a guiding element (12) which is arranged on the guiding carriage (8) for the advancing movement (9) and the cutting movement (10) of the object head (11) and is oriented parallel to the direction of advancement (9), in such a way that it can be guided away from the object head (11).