We revisit Holstein's polaron model to derive an extension of the expression for the thermal dependence of the electrical resistivity in the non-adiabatic small-polaron regime. Our analysis relaxes Holstein's assumption that the vibrational-mode energies ℏωk are much smaller than the thermal energy k B T and substitutes a fifth-order expansion in powers of ℏωk/kBT for the linear approximation in the expression for the quasiparticle hopping probability in the original treatment. The resulting expression for the electrical resistivity has the form ρ(T)=ρ 0 T 3/2 exp(E a/k B T-C/T 3+D/T 5), where C and D are constants related to the molecule-electron interaction energy, or alternatively to the polaron binding energy, and the dispersion relation of the vibrational normal modes. We show that experimental data for the La 1-xCa xMnO 3 (x=0.30,0.34,0.40, and 0.45) manganite system, which are poorly fitted by the conventional non-adiabatic model, are remarkably well described by the more accurate expression. Our results suggest that, under conditions favoring high resistivity, the higher-order terms associated with the constants C and D in the above expression should taken into account in comparisons between theoretical and experimental results for the temperature-dependent transport properties of transition-metal oxides. © 2014 Sociedade Brasileira de Física.