Boltzmann's equation is used to calculate the DC conductivity of electrons in a quantum well. Deformation potential scattering due to 3D acoustic phonons is considered. The relaxation-time approximation is shown to be inappropriate at low temperatures and a variational method is proposed. At very low temperatures inter-sub-band scattering is prohibited, the sub-bands become decoupled and the quantum size effects are frozen out. In this case the resistivity is found to have the Bloch-Gruneisen T⁵ temperature dependence.