Realization of pyroelectric effect in vacuum provides a possibility to develop a compact and relatively inexpensive electron source. In this article we observed and analyzed the I-V curve of electron flow generated during the pyroelectric effect in lithium tantalate single crystal. The region of the monoenergetic electron flow with a slow change in the peak energy is determined. This phenomenon is accompanied by a current avalanche process. Analysis of the electron spectra and the I-V curve shows that the observed avalanche process and the stabilization of the peak energy occurs due to a sharp increase of secondary electrons in the total electron flow.