For the development of a method capable of predicting single point mutations substantially affecting protein thermostability, we studied the effect of the E85R and R82E mutations on the thermostability of thioredoxins from Escherichia coli (Trx) and Bacillus acidocaldarius (BacTrx), respectively. The basic method of investigation was the molecular dynamics simulation of 3D protein models in an explicit solvent at different temperatures (300 and 373 K). Some thermolabile regions in Trx, BacTrx, and their mutants were revealed by analyzing the temperature effect on the molecular dynamics of the protein molecule. The effect of single point mutations on the temperature changes of the protein conformation flexibility in several thermolabile regions was found. The results of the simulations are in accord with experimental data indicating that the mutation E85R increases Trx thermostability, whereas the mutation R82E decreases BacTrx thermostability. The thermostability of these proteins was revealed to depend on ionic interactions between the thermolabile regions. The single point mutations change the parameters of these interactions and make them more favorable in the E85R-Trx mutant and less favorable in the R82E-BacTrx mutant.