Recent work on understanding why protons migrate with increasing temperature in short, strong hydrogen bonds is extended here to three more organic, crystalline systems. Inelastic neutron scattering and density functional theory based simulations are used to investigate structure, vibrations, and dynamics of these systems as functions of temperature. The mechanism determined in a previous work on urea phosphoric acid of low frequency vibrations stabilizing average crystal structures, in which the potential energy well of the hydrogen bond has its minimum shifted towards the center of the bond, is found to be valid here. The new feature of the N-H...O hydrogen bonds studied in this work is that the proton is transferred from the donor atom to the acceptor atom. Molecular dynamics simulations show that in an intermediate temperature regime, in which the proton is not completely transferred, the proton is bistable, jumping from one side of the hydrogen bond to the other. In the case of 3,5-pyridine dicarboxylic acid, which has been studied in most detail, specific phonons are identified, which influence the potential energy surface of the proton in the short, strong hydrogen bond.