DINS is capable of observing coherent tunneling of protons in a double well potential through the effects of the tunneling on the momentum distribution of the protons. In our previous experiment at VESUVIO two years ago we demonstrated this capability in a simple double well system, hydrogen in the interstitial sites of alpha-Mn. The oscillations in the momentum distribution, analogous to the diffraction pattern in a two slit experiment, were clearly seen at 2 K and disappeared at 290 K, when the temperature greatly exceeds the tunnel splitting (6.3 meV). We propose here to study the temperature dependence of the momentum distribution of H in alpha-Mn at intermediate temperatures, and the momentum distribution of deuterium in alpha-Mn, which occupies a similar positions in the lattice, but has ~4 times smaller tunnel splitting of the vibrational ground state, compared to hydrogen.