The invention relates to a method for stamping a non-planar surface (14) of a body (1) with a transfer layer of a hot-stamping foil (5), in which a stamping region of the hot-stamping foil (5) is brought into abutment against the surface (14) of the body (1) and a heated stamping die (3) is pressed against the hot-stamping foil (5) and the surface (14) of the body (1) such that, in the stamping region, the transfer layer detaches from a support of the hot-stamping foil (5) and adheres to the surface (14) of the body (1). In the invention, the hot-stamping foil (5) is pre-heated in a region comprising the entire stamping region before the stamping procedure, in particular by a heating apparatus (6) which is insertable and withdrawable into the device.