  Superfluids can transport heat via simultaneous opposite flows of their
spatially interpenetrating condensate and thermal components. While this
internal convection is usually described within Landau's phenomenological two
fluid hydrodynamics, we apply quantum kinetic theory to a dilute Bose gas held
beween thermal reservoirs at different temperatures, and show that the
phenomenon also appears in collisionless kinetic regimes, and should be
directly observable in currently feasible experiments on trapped ultracold
vapors.
