We propose to use the bi-Maxwellian electron distribution function (EDF) to describe the characteristics of the electron gas in the ionosphere. Such EDF allows one to simulate almost all EDFs found in practice by changing the ratio between the temperatures and densities of two groups of electrons. As a result, this made it possible to obtain simple analytical formulas for calculating the heating of Maxwellian thermal electrons by fast ones. It is shown that the linearized representation of the interelectron collision integral obtained for a one-temperature EDF is not suitable for calculating the heating of electrons in a two-temperature EDF.