A process for transferring a thin layer consisting of a first material to a support substrate consisting of a second material having a different thermal expansion coefficient, comprises providing a donor substrate composed of an assembly of a thick layer formed of the first material and of a handle substrate having a thermal expansion coefficient similar to that of the support substrate, and the donor substrate having a main face on the side of the thick layer introducing light species into the thick layer to generate a plane of weakness therein and to define the thin layer between the plane of weakness and the main face of the donor substrate; assembling the main face of the donor substrate with a face of the support substrate; and detachment of the thin layer at the plane of weakness, the detachment comprising application of a heat treatment.