Ab-initio Density Functional Theory has been used to compute phonons for interstitial hydrogen in α-iron. In the harmonic approximation, these phonons yield Helmholtz's free energy as a function of temperature, which can be used to obtain diffusion barriers from an Arrhenius plot. By comparing with the experimental database compiled by Kiuchi and McLellan, we show that the role of phonons is crucial to understand the diffusion of interstitial hydrogen at T > 300 K. The computed specific heat for Fe16H and Fe behaves quite differently due to the appearance of optical modes and could be used to calibrate the amount of interstitials in the iron matrix.