This assembly comprises a cup containing a thermally-expandable material, a piston designed to move in translation along an axis (X-X) under the action of the thermally-expandable material, a guide (40) for guiding the piston and intended to be fixed to the cup, and a buffer (60) made of an elastomer material and designed to be interposed between the thermally-expandable material and the piston. The guide is provided with a bore (41) that is intended to be centered on the axis and comprises a first bore portion (41.2) having a constant cross-section, a second bore portion (41.1) provided to receive the piston and having a cross-section that is both constant and smaller than that of the first bore portion, and a third bore portion (41.3) that continuously connects the first and second bore portions. According to the invention, the buffer consists of both first and second end portions (62, 61), which, in the assembled state of the thermostatic element, are respectively received in the first and second bore portions regardless of the translational position of the piston, and of a running portion (63), which coaxially connects the first and second end portions and which, before assembly of the buffer to the rest of the thermostatic element, is at least locally thinner relative to the first end portion, so that, in the assembled state of the thermostatic element, the running portion passes from one to the other of the first and second boring portions, via the third boring portion, and partially releases the internal deformation stresses of the buffer when the piston is translated.