By using scanning tunneling microscopy (STM) we have studied the growth of the unfaulted 1 x 1 reconstructed H-terminated domains on the expense of the surface area of the faulted 1 x 1 domains upon adsorption of atomic H on Si(1 1 1)7 x 7. In contrast to previous investigations, we describe the transformation of the surface towards a one-domain H-terminated structure in 1 x 1 geometry as a thermally activated process which is not directly induced by H adsorption. The limitations in achieving a perfect surface are related to the beginning desorption of H at around 680 K.