The invention provides tooling (100) for acting during heat treatment to support a preform (110) of a three-dimensional part obtained by shaping a metal or ceramic powder, the preform presenting at least one bearing surface (112) on which it can rest and at least one suspended surface (111) that is suspended relative to the bearing surface, the tooling comprising a tray (120), and a plurality of blocks (130) arranged on the tray and each having at least one surface (130a) for supporting the preform, the blocks being suitable for moving relative to one another by sliding on the tray between a first position in which the blocks are spaced apart from one another and together define a first volume, and a second position in which the blocks together define a second volume that is smaller than the first volume. The invention also provides a method of heat treating a preform made of powder and using such tooling.