We have studied transverse thermomagnetic effects in a quantum well (QW) with parabolic potential in the presence of a magnetic field parallel to the two-dimensional electron gas layer. The calculation was carried out for the case of elastic electron scattering on short-range potential for degenerate and non-degenerate electron gas. It is shown that the reviewed mechanism of charge carriers' relaxation is essential for the electroconductivity at low temperatures. In the quantum limit, the dependencies of the transverse Nernst-Ettingshausen coefficient and the thermopower on the magnetic field strength, the temperature and the carrier density are determined and analyzed. We have showed that the magnetothermopower is not determined by the entropy only, as is the case for bulk specimens.