The testing of a lightweight unimorph-type deformable mirror (DM) for wavefront correction in cryogenic instruments is reported. The presented mirror manufactured from the titanium alloy TiAl6V4 with a piezoelectric disk actuator was cooled to 86 K and characterized for thermally induced deformation and the achievable piezoelectric stroke between room temperature and 86 K. Through a finite element analysis, we obtained a first approximation in determining the exact temperature-dependent coefficient of thermal expansion (CTE) of the piezo material PIC151. Simulations were based on dilatometer measurements of the CTE of the TiAl6V4 mirror base between room temperature and 86 K. These investigations will enable the improvement of the athermal design of a unimorph-type DM