Temperature quench echoes are analyzed in terms of the temperature-temperature correlation function in the harmonic approximation, and the resulting expressions are compared with molecular dynamics simulations. The relationship between the time dependence of the echo depth and the density of states is demonstrated for harmonic systems. For a protein, which has significant anharmonicity, the time dependence is dominated by relaxation effects that originate from dephasing of the periodic motions. A simple relaxation model is shown to provide a good description of the results observed in the simulations.