The source of increased stability in proteins from organisms that thrive in extreme thermal environments is not well understood. Previous experimental and theoretical studies have suggested many different features responsible for such thermostability. Many of these thermostabilizing mechanisms can be accounted for in terms of structural rigidity. Thus a plausible hypothesis accounting for this remarkable stability in thermophilic enzymes states that these enzymes have enhanced conformational rigidity at temperatures below their native, functioning temperature. This study investigates the relationship between thermostability and rigidity using rubredoxin as a case study. The FIRST software is used to calculate local (residue level) and global rigidity for available rubredoxin structures and simulated mutants. Quantitative global rigidity measures indicate that an increase in structural rigidity (equivalently a decrease in flexibility) corresponds to an increase in thermostability. At the level of individual residues, hydrogen deuterium exchange experiments level indicate differential changes in flexibility between mesophilic and thermophilic rubredoxin structures that agree with computational flexibility analysis from the FIRST software.