  I discuss heat and momentum transport in a mesoscopic film of $^3$He,
confined by rough walls in the normal Fermi liquid state. Inelastic binary
quasiparticle scattering mediated by elastic scattering from the surface
roughness gives rise to a coherent "mixed"scattering channel that drives
anomalous transport over a range of temperature. I calculate the thermal
conductivity and viscosity of the film in this regime and derive these in terms
of the film thickness and autocorrelation function of the surface roughness,
which enters the formulation as an independent input. This calculation can be
useful in understanding and isolating the effects of confinement and surface
roughness, especially in the context of exploring the superfluid state in the
film.
