The thermal accommodation coefficient $\alpha$ has been assumed, although lacking any experimental proof, to be near unity for most gases so far, which denotes no influence. However, it plays a contributing role in the field of the effective thermal conductivity of highly porous insulation materials based on $SiO_2$ or $CaSiO_3$ as it is shown in this work. Besides, this work investigates a possible influence on $\alpha$ for $Ar, N_2, He$ within parameters like temperature, roughness and contamination as this has not been examined on such materials so far. More importantly, it answers the question whether the assumption of $\alpha$ = 1 is valid. By using a parallel plates device, very similar to the guarded-hot-plate, following EN 12667 it was possible to determine $\alpha$ on a dense $CaSiO_3$. It occured that the assumptions $\alpha$ = 1 (for $Ar, N_2$) and $\alpha$ = 0.3 (for $He$) are valid for measurements near room temperature. Further, physical adsorption was found to increase $\alpha$. The determination of the influence of roughness has been started showing an interesting effect, but it still remains an open topic. In a collaborative study molecular dynamics (MD) simulations were performed showing a strong equivalence of $\alpha$ between $SiO_2$ and $CaSiO_3$. These results can be considered a lower limit of $\alpha$ as neither roughness nor adsorption processes have been included in the simulation. Therefore, any deviations between experiments and MD could be considered as an appearance of physical adsorption.