Polished W discs exposed to pure He plasma in the PISCES-B linear-divertor-plasma simulator at 1120 and 1320 K are found to develop deeply nanostructured surface layers consisting of a conglomerate of amorphous 'nanorods'. The growth of the thickness of the nanostructured layer is explored for exposure times spanning 300–(2.2 × 10⁴) s in He plasmas of density n_e ~ 4 × 10¹⁸ m⁻³ and temperature T_e ~ 6–8 eV where the average He-ion surface-impact energy is ~60 eV, below the threshold for physical sputtering. A nanostructured layer in excess of 5 µm thick is observed for the longest exposure time explored. The kinetics of the layer growth are found to follow Fick's law, characterized by an effective diffusive mechanism with coefficients of diffusion: D_{1120 K} = 6.6 ± 0.4 × 10⁻¹² cm² s⁻¹ and D_{1320 K} = 2.0± 0.5 × 10⁻¹¹ cm² s⁻¹. The diffusion of He atoms in W is considered too rapid to explain the observed growth of surface modification and points to the interplay of other mechanisms, such as the availability of thermal vacancies and/or the slower diffusion of He through the forming nanostructured layer.