We report an analysis of high-resolution quasielastic neutron scattering spectra from Myelin Basic Protein (MBP) in solution, comparing the spectra at three different temperatures (283, 303, and 323 K) for a pure D2O buffer and a mixture of D2O buffer with 30% of deuterated trifluoroethanol (TFE). Accompanying experiments with dynamic light scattering and Circular Dichroism (CD) spectroscopy have been performed to obtain, respectively, the global diffusion constant and the secondary structure content of the molecule for both buffers as a function of temperature. Modeling the decay of the neutron intermediate scattering function by the Mittag-Leffler relaxation function, ϕ(t) = Eα(-(t/τ)α) (0 < α < 1), we find that trifluoroethanol slows down the relaxation dynamics of the protein at 283 K and leads to a broader relaxation rate spectrum. This effect vanishes with increasing temperature, and at 323 K, its relaxation dynamics is identical in both solvents. These results are coherent with the data from dynamic light scattering, which show that the hydrodynamic radius of MBP in TFE-enriched solutions does not depend on temperature and is only slightly smaller compared to the pure D2O buffer, except for 283 K, where it is much reduced. In accordance with these observations, the CD spectra reveal that TFE induces essentially a partial transition from β-strands to α-helices, but only a weak increase in the total secondary structure content, leaving about 50% of the protein unfolded. The results show that MBP is for all temperatures and in both buffers an intrinsically disordered protein and that TFE essentially induces a reduction in its hydrodynamic radius and its relaxation dynamics at low temperatures.