In this work, we study dynamical properties-of an extremophilic protein, Initiation Factor 6 (IF6), produced by the archeabacterium Methanocaldococcus jannascii, which thrives close to deep-sea hydrothermal vents where temperatures reach 80 degrees C and the pressure, is up to 750 bar. Molecular dynamics simulations (MD) and quasi-elastic neutron scattering (QENS) measurements give new insights into: the dynamical properties of this protein with respect to its eukaryotic and mesophilic homologue. Results obtained by MD are supported by QENS data and Are interpreted within the framework of a fractional Brownian dynamics model for the characterization of protein relaxation dynamics. IF6 from M. jannaschii at high temperature and pressure shares similar flexibility with its eukaryotic homologue from S. cerevisieae tinder ambient conditions. This work shows for the first time, to our knowledge, that the very common pattern of corresponding states for thermophilic protein adaptation can be extended to thermo-barophilic proteins. A detailed analysis of dynamic properties and of local structural fluctuations reveals a complex pattern for "corresponding" structural flexibilities. In particular, in the case of IF6, the latter seems to be strongly related to the entropic contribution given by an additional, C-terminal, 20 amino-acid tail which is evolutionary conserved in all mesophilic IF6s.