In artificial intelligence, a relaxation of a problem is an overapproximation whose solution in every state of an explicit search provides a heuristic solution distance estimate. The heuristic guides the exploration, potentially shortening the search by exponentially many search states. The big question is how a good relaxation for the problem at hand should be derived. In model checking, overapproximations are called abstractions, and abstraction refinement is a powerful method developed to derive approximations that are sufficiently precise for verifying the system at hand. In our work, we bring these two paradigms together. We pioneer the application of (predicate) abstraction refinement for the generation of heuristic functions that are intelligently adapted to the problem at hand. We investigate how an abstraction refinement process for generating heuristic functions should differ from the process used in the verification context. We do so in the context of DMC of timed automata. We obtain a variety of interesting insights about this approach.