In this paper diffusion of a dilute solution of elastic dumbbell model macromolecules under nonisothermal conditions is studied. Using the center of mass definition for the local polymer concentration, the diffusive flux contains a thermal diffusion dyadic d(T). To get some idea of thermal diffusion d(T) is evaluated for steady state isothermal conditions. Explicit results are presented for some homogeneous flows. It is shown that if the polymeric number density is defined via the beads (of the dumbbell) - termed n(b) - then the diffusive flux j contains partial derivative/partial derivative r . tau(c), where tau(c) is the intramolecular contribution to the bulk stress. Though the form of the diffusion equation for nh thus differs from the corresponding one for n, it is shown that for essentially unbounded systems differences between n and nb are small. Since the results involve the translational diffusion coefficient they can readily be taken over for Rouse coils.