Computer-controlled spatial modulation of coherent light has enabled multiple new ways of imaging through complex media. MEMS-based digital micromirror devices (DMDs) employed as spatial light modulators present considerably higher display frame rates compared to the popular alternative based on liquid crystal technology. For a progress beyond laboratory conditions, the digital hologram projected with a DMD needs to remain time-invariant after the wavefront correction. The thermal load of the DMD when operating at the highest display frame rates is one of the main sources of wavefront deviations that significantly impacts the imaging performance over time. In this work, we studied the wavefront deviations induced by temperature variation of the DMD, and show that they correspond to low-order aberrations which can be represented by Zernike polynomials up to the second order. Further, we study their influence on the focussing quality using wavefront shaping on two popular model systems – a highly-scattering diffuser and a multimode optical fibre – and verify a rapid degradation as the DMD temperature departs from the initial calibration temperature. By actively controlling and stabilizing the temperature of the DMD with a thermoelectric cooler, we demonstrate that the stability of high-speed DMD-based wavefront shaping systems can be greatly extended in time, without the need for recalibration.