Deployable optics promise a revolution in the capability of observing the universe by delivering drastically reduced mass and volume needs for a desired level of performance compared to their conventional counterparts. However, this places new demands on the mechanical and thermal designs of new telescopes, essentially trading mass and volume for structural and control complexity. We compile the thermomechanical challenges that should be taken into consideration when designing optical space systems, as well as summarize 14 projects proposed to address them. Stringent deployment repeatability requirements demand low hysteresis, whereas stability requirements require high stiffness, proper thermal management, and active optics.