Note on the thickness of the Cartesian product of a complete graph and a path

We determine the thickness of the Cartesian product $K_{6p+4}\mathrm{\square }{P}_2$ for $p\ge 0$ and of the Cartesian product $K_8\mathrm{\square }{P}_m$ for $m\ge 1$, where $K_n$ and $P_m$ denote the complete graph on $n$ vertices and the path on $m$ vertices, respectively.