A recent iteration of fluorescence correlation spectroscopy (FCS), z-scan FCS, has drawn attention for its elegant solution to the problem of quantitative sample positioning when investigating two-dimensional systems while simultaneously providing an excellent method for extracting calibration-free diffusion coefficients. Unfortunately, the measurement of planar systems using (FCS and) z-scan FCS still requires extremely mechanically stable sample positioning, relative to a microscope objective. As axial sample position serves as the inherent length calibration, instabilities in sample position will affect measured diffusion coefficients. Here, we detail the design and function of a highly stable and mechanically simple inverted microscope stage that includes a temperature controlled liquid cell. The stage and sample cell are ideally suited to planar membrane investigations, but generally amenable to any quantitative microscopy that requires low drift and excellent axial and lateral stability. In the present work we evaluate the performance of our custom stage system and compare it with the stock microscope stage and typical sample sealing and holding methods.