In a glitch, some energy must be liberated in the neutron star interior. We examine the thermal response of a neutron star to a sudden energy release in the interior. A part of the released energy diffuses outward and is emitted promptly as thermal afterglow from the surface of the star. The appearance of the thermal afterglow exhibits significant variations depending on the magnitude and depth of the energy release and on the equation of state for dense matter. We especially show how the thermal response varies according to whether the released energies are a small or large fraction of the heat content of the star. We also discuss how observations of thermal afterglow can be used to set constraints on the transient energy release and on the equation of state.