We investigate the Baber scattering problem in two dimensions, for the resistivity of a two-band model. The circular Fermi surface is two sheeted, light s electrons scatter against heavy d electrons characterized by a Fermi temperature ${\mathit{T}}_{\mathit{F}}$(d). For T≫${\mathit{T}}_{\mathit{F}}$(d) a saturation of the temperature dependence is expected, whereas for T≪${\mathit{T}}_{\mathit{F}}$(d) a Fermi-liquid behavior is recovered. The details of the crossover are studied by analytical and numerical methods. At low temperatures we show the existence of a ${\mathit{T}}^2$ln(${\mathit{T}}^{\mathrm{*}}$/T) behavior for the case of commensurate density, ${\mathit{k}}_{\mathit{s}}$=${\mathit{k}}_{\mathit{d}}$, and calculate the ${\mathit{T}}^{\mathrm{*}}$ analytically. In the generic case of noncommensurate density, ${\mathit{k}}_3$≠${\mathit{k}}_{\mathit{d}}$, there is no logarithmic correction. We study the region of validity of the low-temperature expansion by comparing with exact numerical evaluations and find, in many cases, an extremely small domain of validity for the low-temperature expansion. We discuss the possible application of these ideas to high-${\mathit{T}}_{\mathit{c}}$ systems.

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