Thermoelectromagnetic convection (TEMC) is the melt motion driven by the interaction of an externally applied magnetic field and the thermoelectric current due to variations of the absolute thermoelectric power and of the temperature. This paper presents numerical solutions for the three-dimensional TEMC in a simplified model of the floating zone process with a nonaxisymmetric temperature variation over the crystal-melt interface. The axial magnetic field is sufficiently strong that inertial effects are negligible, so that each azimuthal Fourier component of the TEMC can be treated independently. Results are presented for the cos theta and cos(2 theta) components of the TEMC. The results show that a very small deviation from axisymmetry in the temperature produces a very large deviation from axisymmetry in the radial and axial components of the TEMC velocity.