CAN THE FERMI-SURFACE BE SHARPER THAN K(B)T

We consider a ''metal'' with a mean free path possessing a sharp maxim um at the Fermi surface. At finite temperature, the width of this maxi mum is close to k(B)T. We show that the electrical conductivity of thi s system behaves as if the peak of the mean free path remains sharp at finite temperatures. In contrast to the well-known normal situation, the resistivity due to elastic scattering is surprisingly found to be linear in temperature, and the resistivity due to scattering by phonon s is proportional to T-2. This model is proposed to relate to some pro perties of ''doped insulators'', such as cuprates, organic metals and fullerenes.