Under quite natural general assumptions, the following results are obtained. The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. The general structure of the horizon spectrum is found. In the special case of loop quantum gravity, the value of the Barbero-Immirzi parameter is found. The discrete spectrum of thermal radiation of a black hole fits the Wien profile. The natural widths of the lines are much smaller than the distances between them. The total intensity of the thermal radiation is estimated. If the density of quantized primordial black holes is close to the present upper limit on the dark-matter density in our Solar system, the sensitivity of modern detectors is close to that necessary for detecting this radiation.