The paper deals with the mathematical and computer modelling of the induction heating of a thin nonmagnetic slab, whose thickness is very small with respect to its length and width. The task is formulated as a quasi-coupled problem, with respecting the temperature depend-encies of important material parameters (electrical and thermal conductivities and specific heat and mass). The harmonic electromagnetic field producing the Joule losses within the slab is generated by two symmetrically placed inductors of any shape (above and below the slab) and is considered perfectly transversal. As its distribution can hardly be determined by means of the existing finite element techniques due to problems with discretisation caused by the geometrical incommensurability of the particular subregions involved (slab and inductor ver-sus air), an alternative mathematical description has been suggested based on the vector inte-gral equation for the eddy current density in the slab. This vector equation may be decom-posed into four component equations for the real and imaginary parts in two relevant direc-tions. The system is characterised by weakly singular kernel functions and may relatively simply be proved to have a unique solution. The originally continuous model is then discre-tised and solved by any procedure suitable for processing large matrix equations. The distri-bution of the eddy current density within the slab provides the distribution of the specific Joule losses. These represent the input data for the consequent thermal computations. Distri-bution of the temperature in the slab is solved by means of the non-stationary balance equa-tions. In order to cope with the temperature dependencies of the material properties, two it-eration processes (internal and external) have been implemented into the algorithm. The inter-nal process is intended for correction of coefficients in the equation describing the tempera-ture distribution, while the external one corrects the values of electrical conductivity in the respective elements of the mesh covering the slab. The solution provides the time evolution of different quantities (for instance the specific Joule losses or temperature in selected parts of the slab) and may easily be extended by movement of the slab or the inductors. The theoreti-cal analysis is supplemented by an illustrative example.