Capillaries cannot defeat the divergence theorem: If you have a volume where heat is produced but the temperature does not increase, the heat has to leave via the surface. It is true that the surface area available to diffusion can scale at any rate (eg. Menger sponge), but the heat still has to leave the volume via its boundary. In the case of capillaries, this is by convection which means that the product of coolant temperature differential and flow speed has to scale.