This paper studies the magneto-heat coupling model which describes iron loss of conductors and energy exchange between magnetic field and Ohmic heat. The temperature influences Maxwell's equations through the variation of electric conductivity, while electric eddy current density provides the heat equation with Ohmic heat source. It is in this way that Maxwell's equations and the heat equation are coupled together. The system also incorporates the heat exchange between conductors and cooling oil which is poured into and out of the transformer. We propose a weak formulation for the coupling model and establish the well-posedness of the problem. The model is more realistic than the traditional eddy current model in numerical simulations for large power transformers. The theoretical analysis of this paper paves a way for us to design efficient numerical computation of the transformer in the future.