The response of the stratosphere to a weak pole-to-equator surface temperature gradient is examined using a general circulation model with a resolved middle atmosphere. While the eddy kinetic and potential energies of the entire atmosphere decrease markedly when the surface temperature gradient is weakened, the eddy energy in the stratosphere changes little. This is partially attributable to the relative stability of the amount of energy in the largest stationary eddies, but the dynamic response of the lower stratosphere also contributes by altering the refractive index for vertically propagating waves. The pole-to-equator gradient in the height of the tropopause weakens as the surface temperature gradient decreases, limiting the depth to which the polar stratospheric vortex penetrates. In the simulations with a weak surface temperature gradient, the meridional temperature gradients are weaker from through the depth of the troposphere and in the lower stratosphere too, producing weaker mean winds in thermal-wind balance. This allows energy in some shorter stationary eddies to propagate vertically into the stratosphere, ensuring that the residual mean circulation of the winter stratosphere remains strong. The convergence of the Eliassen-Palm Flux in the stratosphere is larger in the simulations with a weak surface temperature gradient than in those with a contemporary one. Temperatures during the polar night remain as far from radiative equilibrium values in simulations using the weak surface temperature gradient as in simulations using a modern one.