In swordfish (Xiphias gladius), the dorsal rectus muscle of the eye (M. rectus dorsalis) is partly differentiated for heat production similar to brown adipocytes. Other parts of the dorsal rectus show a typical muscular structure. This modified muscle and its anatomical relationships to neighboring organs were investigated using macroscopic dissections, light and transmission electron microscopy, nuclear magnetic resonance tomography, and scanning electron microscopy of vascular corrosion casts. The ophthalmic artery off the efferent pseudobranchial artery supplies the dorsal rectus muscle. The ophthalmic artery branches in a brush‐like manner as it enters the origin of the muscle. In this region, numerous arterioles and venules are arranged in parallel, suggesting a countercurrent heat exchange mechanism. Thermogenic cells, morphologically similar to brown adipocytes, surround small vascular branches in the middle of the muscle. Muscular cells also extend into this area. The vessels then divide into a tree‐like pattern, forming an extensively capillarized area near the surface of the muscle at the basisphenoid bone. The basisphenoid is reduced to a thin connective tissue layer in this area, hence facilitating thermal transfer between the blood in the muscle and the brain base. The Tela lymph‐adiposa surrounds the brain with large masses of fat. Additionally, voluminous masses of periocular fat provide thermal insulation lateral to the lateral rectus muscle of the eye. It is suggested that this system for raising the temperature of areas of the brain a few degrees above ambient temperature allows an optically oriented predator such as the swordfish to respond to optical input in cold water more efficiently. J. Morphol. 234:89–96, 1997. © 1997 Wiley‐Liss, Inc.