  We present the Onsager--Stefan--Maxwell thermodiffusion equations, which
account for the Soret and Dufour effects in multicomponent fluids. Unlike
transport laws derived from kinetic theory, this framework preserves the
structure of the isothermal Stefan--Maxwell equations, separating the
thermodynamic forces that drive diffusion from the force that drives heat flow.
The Onsager--Stefan--Maxwell transport-coefficient matrix is symmetric, and the
second law of thermodynamics imbues it with simple spectral characteristics.
This new approach allows for heat to be considered as a pseudo-species and
proves equivalent to both the intuitive extension of Fick's law and the
generalized Stefan--Maxwell equations popularized by Bird, Stewart, and
Lightfoot. A general inversion process facilitates the unique formulation of
flux-explicit transport equations relative to any choice of convective
reference velocity. Stefan--Maxwell diffusivities and thermal diffusion factors
are tabulated for gaseous mixtures containing helium, argon, neon, krypton, and
xenon. The framework is deployed to perform numerical simulations of steady
three-dimensional thermodiffusion in a ternary gas.
