We have measured the thermal boundary resistance between various configurations of sintered silver and a saturated He-3-He-4 solution between 8 and 150 mK. We observe that there is a length scale involved in the heat flow between sinter and liquid, which manifests itself as a thickness-dependent crossover from a T--1.5 dependence of the resistance at high temperatures to a T-3 behavior at low temperatures. This allows us to extract the Kapitza boundary resistance which we find to vary as T-3, as expected from simple theory, and not as T-2 as suggested by most recent measurements.