  Prompted by results that showed that a simple protein model, the frustrated
G\=o model, appears to exhibit a transition reminiscent of the protein
dynamical transition, we examine the validity of this model to describe the
low-temperature properties of proteins. First, we examine equilibrium
fluctuations. We calculate its incoherent neutron-scattering structure factor
and show that it can be well described by a theory using the one-phonon
approximation. By performing an inherent structure analysis, we assess the
transitions among energy states at low temperatures. Then, we examine
non-equilibrium fluctuations after a sudden cooling of the protein. We
investigate the violation of the fluctuation--dissipation theorem in order to
analyze the protein glass transition. We find that the effective temperature of
the quenched protein deviates from the temperature of the thermostat, however
it relaxes towards the actual temperature with an Arrhenius behavior as the
waiting time increases. These results of the equilibrium and non-equilibrium
studies converge to the conclusion that the apparent dynamical transition of
this coarse-grained model cannot be attributed to a glassy behavior.
