  A new equation, rooted in the theory of Brownian motion, is proposed for
describing heat conduction by phonons. Though a finite speed of propagation is
a built-in feature of the equation, it does not give rise to an inauthentic
wave front that results from the application of the hyperbolic heat equation
(of Cattaneo). Even a simplified, analytically tractable version of the
equation yields results close to those found by solving, through more elaborate
means, the equation of phonon radiative transfer. An explanation is given as to
why both Brownian motion and its inverse (radiative transfer) provide equally
serviceable paradigms for phonon-mediated heat conduction.
