In proteins, the Mössbauer effect and neutron scattering show a broad line and a rapid increase of the conformational mean-square displacement above about 180 K. The increase, dubbed the "dynamical transition," is controversial. We introduce a new interpretation of the Mössbauer effect in proteins and demonstrate that no dynamical transition is required. The increase in the mean-square displacement and the broad line are caused by fluctuations in the protein's hydration shell. Using the dielectric spectrum of these fluctuations, we predict the shape of the Mössbauer spectrum from 80 to 295 K with one dimensionless coefficient.