It has been suggested that structural rigidity is connected to thermostability, e.g. in enzymes from thermophilic microorganisms. We examine the importance of correctly handling salt bridges, and interactions which we term 'strong polars', when constructing the constraint network for global rigidity analysis in these systems. Through a comparison of rigidity in citrate synthases, we clarify the relationship between rigidity and thermostability. In particular, with our corrected handling of strong polar interactions, the difference in rigidity between mesophilic and thermophilic structures is detected more clearly than in previous studies. The increase in rigidity did not detract from the functional flexibility of the active site in all systems once their respective temperature range had been reached. We then examine the distribution of salt bridges in thermophiles that were previously unaccounted for in flexibility studies. We show that in hyperthermophiles these have stabilising roles in the active site; occuring in close proximity to key residues involved in catalysis and binding of the protein.