Micro-Electro-Opto-Mechanical-Systems or MOEMS have potential applications inter alia in biomedical research. For instance, studies of the Bystander Effect require controlled irradiation of biological cells with focused X-rays to reveal the mechanisms occurring. X-ray focusing may be achieved using an adaptive optic micro-lens in which focusing is entirely reflective and therefore compatible with broad band illumination, an improvement over diffractive systems such as zone plates. Such a micro-lens can be microfabricated in the form of a bent-cantilever beam made from two dissimilar materials (polyimide and gold) in a thermal bimorph configuration, actuated with a micro heater. The parallel horizontal slots on the beam provide the transmission and focusing functions, while the heater provides control of the focal length through variation of the beam’s curvature. This novel system has been named 1D-MOXI (Micro-Opto-X-ray Imaging) and a basic system has already been made and tested thermo-mechanically. The present work focuses on details of the geometry of the deformed slotted micro-beam lens element under thermally derived strain, using finite element analysis, and suggests an optimized MOEMS design, giving prescribed curvature of the lens through changing the number and the dimensions of the slots. The study reveals the localized stress and the small deviations of the micro-lens behavior from that of perfect spherical geometry. The focal length variation with temperature is compared with the experimental values and those predicted by an analytical model.