This work reports neutron diffraction and incoherent neutron scattering experiments on N-methylacetamide (NMA), which can be considered the model building block for the peptide linkage of polypeptides and proteins. Using the neutron data, we have been able to associate the onset of a striking negative thermal expansion (NTE) along the a-axis with a dynamical transition around 230 K, consistent with our calorimetric experiments. Observation of the NTE raises the question of possible proton transfer in NMA, which, from our data alone, still cannot be settled. We can only speculate that intermolecular repulsive forces increase as the O center dot center dot center dot H distance decreases upon cooling, and that around 230 K the lattice relaxes without observation of an actual proton transfer. However, the existence of a nonharmonic potential, reflected by the behavior of the phonon vibrations together with the observation of NTE, could be justified by the "vibrational" polaron theory in which a dynamic localization of the vibrational energy is created by coupling an internal molecular mode to a lattice phonon. More generally, this work shows that neutron powder diffraction techniques can be very powerful for investigating structural deformations in small peptide systems.