  In this paper, the generation of magnetic fields in a nonuniformly rotating
layer of finite thickness of an electrically conducting fluid by thermomagnetic
(TM) instability. This instability arises due to the temperature gradient
$\nabla T_0$ and thermoelectromotive coefficient gradient $\nabla\alpha $. The
influence of the generation of a toroidal magnetic field by TM instability on
convective instability in a nonuniformly rotating layer of an electrically
conductive fluid in the presence of a vertical constant magnetic field
${\bf{B}}_0 \| {\rm OZ}$ is established. As a result of applying the method of
perturbation theory for the small parameter $ \epsilon = \sqrt {(\textrm
{Ra}-\textrm {Ra}_c) / \textrm {Ra}_c} $ of supercriticality of the stationary
Rayleigh number $\textrm {Ra}_c$ a nonlinear equation of the Ginzburg-Landau
type was obtained. This equation describes the evolution of the finite
amplitude of perturbations. Numerical solutions of this equation made it
possible to determine the heat transfer in the fluid layer with and without TM
effects. It is shown that the amplitude of the stationary toroidal magnetic
field noticeably increases with allowance for TM effects.
