We study heat transfer through the conductive lithosphere and convective mantle on the basis of a 2-D convection model in order to better understand the differences between Archean and Proterozoic lithospheres. The original improvement in the modeling consists of a precise track of the cutoff temperature between conduction and convection. The conductive lithosphere is undeformable, and the convective mantle has a constant viscosity. The conductive lithosphere in Archean cratons is assumed to have a lower radiogenic heat production in the crust and/or the conductive mantle, and/or a higher cutoff temperature (attributed to a stiffening of the more depleted mantle) relative to Proterozoic terrains. We also investigate the effect of a fourth factor never considered before: an enhancement of the vertical thermal conductivity in the conductive Archean mantle due to a vertical lineation. Our model successfully predicts the observations on the Canadian and South African shields. A high vertical thermal conductivity in the Archean lithospheric mantle possibly associated to a radiogenic crust depletion explains many observations: i.e., (1) the development of a thick Archean cold root, (2) a dipping cold convective plume beneath Archean cratons, (3) a uniform mantle heat flux along Archean and Proterozoic terrains, and (4) strong high seismic velocity anomalies over Archean cratons. In addition, a lower radiogenic heat production of the lithospheric mantle or a larger cutoff temperature in Archean cratons is not favored by our models. Finally, we investigate how a cold root and a sub-Archean cold mantle plume react to the shear induced by large-scale mantle flow and to the collision with a hot mantle plume. Models show that shear removes the cold plume from below the Archean craton, but cold dipping instabilities are periodically generated inside the convective boundary layer below the Archean cratonic lid. However, the thick Archean lithospheric root may survive several orogeneses. In addition, the models show that it takes at least 200 Myr for a hot mantle plume to erode the thick lithospheric root. This suggests that an Archean root may only disappear if the plate remains above a hot plume for a very long time.