The conical diamond is retained in material of specific thermal expansion coefficient to ensure that it is not loosened when the temperature rises. The tool comprises a head which includes a small diamond (2) fixed to a support body (3). The diamond has a conical shape with its base retained in the support body, and its tip projecting freely. The diamond is fastened by a system which avoids the diamond becoming unseated as a result of different thermal expansion of the diamond and base material. This may comprise a seating in the block which is also conical in shape, or may comprises a welding material (5) surrounding the base of the cone, within a recess formed in the block. Materials are chosen such that their respective degrees of thermal expansion do not allow the diamond to become loose when the device is heated.