We investigated the heating of electrons by a strong electric field directed along the plane of the free movement of electrons inside a quantum well with parabolic potential of confinement. We are considered the case of strong degeneracy of the electron gas and the absence of phonon heating. Heating of electrons in a strong electric field leads to a substantial change in the values of thermoelectric and thermomagnetic effects, as well as their dependence on material parameters (electron density and temperature). In addition, it leads to a dependence of the above-mentioned effects on the applied electric field, which makes it possible to control the magnitude of effects by means of electric field. In theoretical calculations of thermoelectric and thermomagnetic effects in the strong electric field, as the first step is to calculate the average electron energy (the effective electron temperature). In this work we have calculated the effective electron temperature of strongly degenerate electron gas in a quantum well with a parabolic confining potential. To calculate the electric current along the plane of the free movement of the electrons was used the Boltzmann equation method. We have taken into account the mechanisms of electron scattering by impurity ions, both deformation and piezoelectric potentials of acoustic phonons. Since, under the circumstances low temperatures, scattering by optical phonons is inefficient, we did not consider this mechanism. In calculating the relaxation times of electrons, we also take into account the screening of scattering potentials. The effective electron temperature found from the balance equation: in the steady state, the energy gained by an electron system from the electric field ( ) 2 σ 2 ϑ E equals the energy transferred Fig. 1. Dependence of dimensionless electron temperature ϑ on the electric field strength at T = 5K (curve 1). Curve 2 and 3 are the results of calculations in the cases ϑ −1 << 1 and ϑ >> 1, respectively. to the phonon system: ( ) 2 ( ) σ 2 ϑ E =Wep ϑ . Here ϑ = Te T is the dimensionless electron temperature, ( ) σ 2 ϑ is the conductivity of two-dimensional electron gas in a strong electric field. In our case the scattering by impurity ions is the main mechanism of scattering of the electron momentum, and the role of the two mechanisms - the deformation and piezoelectric in energy losses are the same order. In the special cases of weak (ϑ −1 << 1) and strong (ϑ >> 1) heating we have found analytical expressions for the electron temperature. It is shown that the temperature of very hot electron gas is a quadratic function of the electric field. In general, the dependence of ϑ on the electric field is found by numerical calculation for the quantum well GaAs/AlxGa1−x As (in numerical calculations used the values of physical parameters taken from [1]). From our numerical calculations, as shown in Fig. 1, it follows that the dependence of ϑ on the electric field is close to a quadratic dependence.