In the attempt to clarify possible mechanisms underlying thermal stability of proteins, we study through molecular dynamics thermophile Bc-Csp, mesophile Bs-CspB, and selected mutants. These proteins have been extensively characterized experimentally; researchers showed that differential thermostability among the wild type proteins is fundamentally linked to one or two mutated amino acids, and that the nature of the effect is electrostatic. They also inferred an atomistic mechanism related to removal of unfavorable interactions, rather than to the formation of salt bridges. Molecular dynamics allows us to confirm and support both hypotheses. Several other collective parameters have also been monitored in relation to thermophilicity, such as global and local rigidity, permanence and number of hydrogen bonds, or of salt links. None of these clearly correlates with the thermal stability of the presently studied proteins.