The temperature dependence of the density of energy states in semiconductors is considered. With the help of mathematical modeling of the thermal broadening of the energy levels, the temperature dependence of the band gap of semiconductors is studied. In view of the non-parabolic and the temperature dependence of the effective mass of the density of states in the allowed bands, graphs of temperature dependence of the band gap are obtained. The theoretical results of mathematical modeling are compared with experimental data for Si, InAs and solid solutions of p-Bi_2-xSb_xTe_3-ySe_y. The theoretical results satisfactorily explain the experimental results for Si and InAs. The new approach is investigated by the temperature dependence of the band gap of semiconductors.