The Curtiss-Bird phase-space kinetic theory of polymers is used to derive an expression for the thermal conductivity of a dilute polymer solution, with the polymers represented as arbitrary bead-spring models. Then the general expression is specialized to Rouse bead-spring chains (with Hookean springs). The resulting expression contains several momentum-space averages as well as the configuration-space distribution function for the polymer chains. Use is made of the authors' previous work on the solution of the Fokker-Planck equation for arbitrary bead-spring models to evaluate the momentum-space averages. Then two special cases are considered: (a) the Hookean dumbbell model, in a fluid with velocity,gradients, and (b) the Rouse chain model, with the fluid at rest. For the latter, the authors' previous study of the properties of tensor Hermite polynomials is helpful for solving the partial differential equation for the configurational distribution function for a polymer molecule in a fluid with a constant imposed temperature gradient. It is shown how the Gaussian distribution function is distorted in a nonisothermal system, but this distortion contributes only about 5% to the final value of the thermal conductivity. The results for the Rouse chain are compared with those previously obtained for several dumbbell models. (C) 1997 American Institute of Physics.