A theoretical model is proposed for the evaluation of dielectric properties of the cell nucleus between 0.3 and 3 GHz, as a function of its nucleic acids (NA) concentration (CNA). It is based on literature data on dielectric properties of DNA solutions and nucleoplasm. In skeletal muscle cells, the specific absorption rate (SAR) ratio between nucleoplasm and cytoplasm is found to be larger than one for CNA above 30 mg/ml. A nearly linear relationship is found between CNA and this nucleocytoplasmic SAR ratio. Considering the nanoscale of the layer of condensed counterions and bound water molecules at the NA-solution interface, the power absorption per unit volume is evaluated at this precise location. It is found to be between one and two orders of magnitude above that in muscle tissue as a whole. Under realistic microwave (MW) exposure conditions, however, these SAR inhomogeneities do not generate any significant thermal gradient at the scale considered here. Nevertheless, the question arises of a possible biological relevance of nonnegligible and preferential heat production at the location of the cell nucleus and of the NA molecules.