Here we seek to understand the higher frequency of occurrence of salt bridges in proteins from thermophiles as compared to their mesophile homologs. We focus on glutamate dehydrogenase, owing to the availability of high resolution thermophilic (from Pyrococcus furiosus) and mesophilic (from Clostridium symbiosum) protein structures, the large protein size and the large difference in melting temperatures. We investigate the location, statistics and electrostatic strengths of salt bridges and of their networks within corresponding monomers of the thermophilic and mesophilic enzymes. We find that many of the extra salt bridges which are present in the thermophilic glutamate dehydrogenase monomer but absent in the mesophilic enzyme, form around the active site of the protein. Furthermore, salt bridges in the thermostable glutamate dehydrogenase cluster within the hydrophobic folding units of the monomer, rather than between them. Computation of the electrostatic contribution of salt bridge energies by solving the Poisson equation in a continuum solvent medium, shows that the salt bridges in Pyrococcus furiosus glutamate dehydrogenase are highly stabilizing. In contrast, the salt bridges in the mesophilic Clostridium symbiosum glutamate dehydrogenase are only marginally stabilizing. This is largely the outcome of the difference in the protein environment around the salt bridges in the two proteins. The presence of a larger number of charges, and hence, of salt bridges contributes to an electrostatically more favorable protein energy term. Our results indicate that salt bridges and their networks may have an important role in resisting deformation/unfolding of the protein structure at high temperatures, particularly in critical regions such as around the active site.