Thermal effects are important to take into account when designing high-precision optical instruments for space, as thermal deformation can cause significant misalignment errors. Another important factor to consider are vibrations introduced during the launch as well as during operation, which translate into eigenfrequency requirements. These design requirements are difficult for an engineer to satisfy, as their complex physics occlude the impact that specific design choices have on the resulting dynamic and thermo-elastic responses. Using combinations of multiple materials potentially offers advantages, but also further increases the design challenge. Topology optimization (TO) is a powerful computational design tool that can aid in this process. TO can also be extended to include multiple materials, which holds the promise of reaching higher levels of performance. We investigate the benefits of multi-material TO for the design of thermally stable optical mounts. Vibration requirements are translated into an eigenfrequency constraint, while the optimization objective is minimizing mass. We also investigate mitigating optical aberrations induced by different thermal scenarios with the same design. To compare the resulting designs we investigate their respective objective values, as well as newly proposed measures of non-discreteness adapted to multi-material TO. The results show that when thermo-mechanical stability is harder to achieve, multi-material TO offers improved performance compared to single material solutions. However, for less demanding cases undesired interface behaviour starts to influence the multi-material results, which causes single material TO to outperform multi-material TO.