The low‐temperature electrical resistivity in thin plates has been theoretically examined. It is shown that the bulk relaxation time τi is a reasonable approximation to describe the impurity scattering. In constrast, the low‐temperature phonon‐electron interaction is not properly described by the bulk thermal relaxation time τp. Nevertheless, expressions have been obtained for the Fermi function in thin plates correct to first order in τi/τp≪1. The predicted temperature‐dependent resistivity obtained is smaller than the results predicted by Fuchs, which are also given explicitly in this limit for the first time. In the limit of very low temperatures and very thin plates a temperature dependence of resistivity greater than the bulk value, but ⅔ that obtained by Fuchs, is predicted. These results are discussed.