A cholesteric liquid crystal lacks a center of inversion and it is consequently different from its mirror image. The low symmetry allows linear cross couplings between thermodynamic forces and fluxes that are polar vectors and pseudovectors, respectively. This makes it possible for a temperature gradient, which is a polar vector to induce a director angular velocity, which is a pseudovector. The reverse is also possible; the torque conjugate to the director angular velocity can drive a heat current. This is the basis for the Lehman effect where a temperature gradient parallel to the cholesteric axis causes the local director to rotate. We use linear response theory to derive Green-Kubo relations and nonequilibrium molecular dynamics simulation algorithms for the transport coefficient that couples the temperature gradient and the director angular velocity. The theory is completely general and can consequently be used to find relations for any linear cross coupling coefficient between a polar vector and a pseudovector.