A demonstrator adaptive optics-system with a thermally actuated active mirror (AM) is presented to pre-study feasibility of sub-nm wavefront control in extreme ultraviolet (EUV) lithography. The AM is thermally actuated by selective heating using a spatial controllable heat source. Four different methods have been implemented to control the deformation of the AM. First thermal feedforward using estimated state feedback (ESF), second thermal feedback using proportional integral (PI) control, third their combination and fourth deformation feedback using PI control. To support ESF, a thermo-elastic finite element model is employed that describes the thermal deformation of the AM. ESF shows satisfying performance with a time constant of 10 s and a residual error of 0.7 nm. Thermal feedback shows large fluctuations of 12 nm for spherical aberrations of due to feedback of noise from the thermal camera. By applying deformation feedback the RMS-error is reduced to a satisfying 0.25 nm. This study shows that deformation control of this AM can be realised using thermal feedforward and deformation feedback to meet the requirements for EUV lithography.@en