Variational principles and Mutter's form of the entropy inequality are used to establish the balance laws and constitutive equations for thermorigid dielectrics. An isotropy integrity basis that depends on the polarization-gradient tensor, polarization vector, and temperature-gradient vector is constructed for the free-energy function, and its minimality is verified. Representations for the entropy-flux vector and the heat-flux vector, when substituted into the restrictions derived from the entropy inequality, lead to the conclusions that the coldness function A depends on polarization and that the commonly known relation for isotropic materials, according to which the entropy-flux vector is equal to the ratio of heat flux to temperature, is not valid for polarized materials.