  We introduce a combinatorial curvature flow for PL metrics on compact
triangulated 3-manifolds with boundary consisting of surfaces of negative Euler
characteristic. The flow tends to find the complete hyperbolic metric with
totally geodesic boundary on a manifold. Some of the basic properties of the
combinatorial flow are established. The most important ones is that the
evolution of the PL curvature satisfies a combinatorial heat equation. It
implies that the total curvature decreases along the flow. The local
convergence of the flow to the hyperbolic metric is also established if the
triangulation is isotopic to a totally geodesic triangulation.
