Among the tremendous diversity of fish, there are a small number that are considered elite in their swimming performance. These include representatives from the tunas, billfish and sharks. In addition to being elite swimmers, these fish share numerous specialized anatomical features including the structure of their swimming muscles and some form of regional endothermy, termed heterothermy. These heterothermies fall into two classes: those that maintain elevated temperatures in swimming muscles and those that have muscle-derived tissues specialized for delivering warm blood to the brain. Because these versions of heterothermy are manifest in fish whose swimming performance is considered elite, it has been parsimonious to hypothesize that heterothermy is part of an integrated high-performance design. Recognizing that the design of skeletal muscle is hierarchical, the design of heterothermic muscle in fish will be examined within a hierarchical framework. This paper will examine, in order, the specific anatomical specializations, the performance of muscle as a biomaterial and then as a dynamic mechanical structure or device - in each case looking at the extent to which heterothermy is part of an integrated high-performance design or is perhaps just a happy accident. This examination will reveal how difficult it is to make a case for the central importance of heterothermy in the design of these swimming muscle systems.