A detailed study of the thermal behaviour of atomic motions in the organic ferroelectric croconic acid is presented in the temperature range 5-300 K. Using high-resolution inelastic neutron scattering and first-principles electronic-structure calculations within the framework of density functional theory and a quasiharmonic phonon description of the material, we find that the frequencies of the well defined doublet in inelastic neutron scattering spectra associated with out-of-plane motions of hydrogen-bonded protons decrease monotonically with temperature indicating weakening of these bonding motifs and enhancement of proton motions. Theoretical mean-square displacements for these proton motions are within 5% of experimental values. A detailed analysis of this observable shows that it is unlikely that there is a facile proton transfer along the direction of ferroelectric polarization in the absence of an applied electric field. Calculations predict constrained thermal motion of proton along crystallographic lattice direction c retaining the hydrogen bond motif of the crystal at high temperature. Using the Berry-phase method, we have also calculated the spontaneous polarization of temperature dependent cell structures, and find that our computational model provides a satisfactory description of the anomalous and so far unexplained rise in bulk electric polarization with temperature. Correlating the thermal motion induced lattice strain with temperature dependent spontaneous polarizations, we conclude that increasing thermal strain with temperatures combined with constrained thermal motion along the hydrogen bond motif are responsible of this increase in ferroelectricity at high temperature.