Experiments on the dynamics of vibrational fluctuations in myoglobin revealed an interesting behavioral cross-over occurring in the range of 180-200 K. In this temperature range the mean square displacement of atomic positions versus temperature sharply increases its slope indicating the dissociation of CO from the haeme group. In this paper we develop a theoretical framework for the description of this phenomenon assuming the existence of an effective quartic potential. We then use non-Gaussian statistics to obtain a relationship between the mean square displacement and model parameters. We compare our model to published experimental data using a physically meaningful parameter fit. While the Gaussian approximation's applicability is verified by the low-temperature régime, in the high-temperature limit deviations from the Gaussian approximation are due to the double-well nature of our effective potential. In the second part of the paper we summarize our molecular dynamics simulations of the myoglobin's hydration in the low-temperature régime and at room temperature.