The properties of equilibrium thermoelectron clouds surrounding dust particles with large surface charge density were studied based on a rigorous solution of the Poisson-Boltzmann equation in a planar case. According to this theory, an equilibrium charge of a particle is markedly lower than the values obtained in the experiment. It is suggested that the thermoemissive dust plasma studied in experiments is supercooled with respect to the degree of ionization. (C) 2000 MAIK "Nauka/Interperiodica".