Energy and momentum transport in a strongly sheared dilute gas is analyzed in the context of the nonlinear Boltzmann equation. Thermal transport is generated in the system by the action of a nonconservative external force which tries to mimick the effects of a temperature gradient. By performing a perturbation expansion in powers of the field strength, we obtain expressions for the field susceptibility tensor and the shear viscosity coefficient up to second order in the force. They are highly nonlinear functions of the shear rate. It is shown that the choice of the heat field used in computer simulations yields a field susceptibility tenser different from the thermal conductivity tenser. In order to get equivalent results, a new shear-rate dependent force is suggested. The calculations presented here extend previous results derived from the Bhatnagar-Gross-Krook approximation [J. Chem. Phys. 101, 1423 (1994)].