We investigate the phenomenon of pyroelectric luminescence in LiNbO3 single crystals. This faint emission of light due to temperature-induced changes of permanent polarization is induced by different types of charge carrier recombination, outside and inside the crystal. With decreasing atmospheric pressure, the external discharge mechanism transitions from sparse intense gas discharge pulses at ambient pressure, to frequent faint discharges close to 1 mbar, to a continuous emission which is referred to as smooth pyroelectric luminescence. Our experimental setup exposes the crystal to constant positive and negative temperature changes in the range of 360-450 K under high vacuum while simultaneously measuring the surface charge density and the emitted intensity. A microscopic model of the luminescence allows the description of the time-dependent pyroelectric luminescence, in particular the determination of deep trap potentials that are otherwise inaccessible to thermal ionization. Using this model, we show that the behavior of this emission in LiNbO3 crystals is consistent with the release of trapped electrons by the Poole-Frenkel effect from a Dirac-well potential, while the commonly assumed coulombic trap shape is in clear disagreement with both the temporal evolution of the emission as well as the magnitude of the electric field obtained in our measurements.