In this work, we consider open-boundary conditions at high temperatures, as they can potentially be of help to measure the topological susceptibility. In particular, we measure the extent of the boundary effects at $T=1.5T_c$ and $T=2.7T_c$... In the first case, it is larger than at $T=0$ while we find it to be smaller in the second case. The length of this "boundary zone" is controlled by the screening masses. We use this fact to measure the scalar and pseudo-scalar screening masses at these two temperatures. We observe a mass gap at $T=1.5T_c$ but not at $T=2.7T_c$. Finally, we use our pseudo-scalar channel analysis to estimate the topological susceptibility. The results at $T=1.5T_c$ are in good agreement with the literature. At $T=2.7T_c$, they appear to suffer from topological freezing, impeding us from providing a precise determination of the topological susceptibility. It still provides us with a lower bound, which is already in mild tension with some of the existing results. (read more)