Molecular machines or macromolecular complexes are supramolecular assemblies of biomolecules with a variety of functions. Structure determination of these complexes in a purified state is often tedious owing to their compositional complexity and the associated relative structural instability. To improve the stability of macromolecular complexes in vitro, we present a generic method that optimizes the stability, homogeneity and solubility of macromolecular complexes by sparse-matrix screening of their thermal unfolding behavior in the presence of various buffers and small molecules. The method includes the automated analysis of thermal unfolding curves based on a biophysical unfolding model for complexes. We found that under stabilizing conditions, even large multicomponent complexes reveal an almost ideal two-state unfolding behavior. We envisage an improved biochemical understanding of purified macromolecules as well as a substantial boost in successful macromolecular complex structure determination by both X-ray crystallography and cryo-electron microscopy.