  $SU(N)$ gauge theories on compact spaces have a non-trivial vacuum structure
characterized by a countable set of topological sectors and their topological
charge. In lattice simulations, every topological sector needs to be explored a
number of times which reflects its weight in the path integral. Current lattice
simulations are impeded by the so-called freezing of the topological charge
problem. As the continuum is approached, energy barriers between topological
sectors become well defined and the simulations get trapped in a given sector.
A possible way out was introduced by L\"uscher and Schaefer using open boundary
condition in the time extent. However, this solution cannot be used for thermal
simulations, where the time direction is required to be periodic. In this
proceedings, we present results obtained using open boundary conditions in
space, at non-zero temperature. With these conditions, the topological charge
is not quantized and the topological barriers are lifted. A downside of this
method are the strong finite-size effects introduced by the boundary
conditions. We also present some exploratory results which show how these
conditions could be used on an algorithmic level to reshuffle the system and
generate periodic configurations with non-zero topological charge.
