In swordfish and some other billfishes, part of the superior rectus eye muscle has lost its contractile function and become a heat-generating tissue rich in mitochondria. Blood serving the eyes and brain passes through a vascular exchanger next to it, so those organs stay warm while the rest of the body cools to ambient temperature.
The payoff is temporal resolution. Cold retinas respond sluggishly, and experiments on billfish eyes have shown that flicker fusion frequency, a measure of how quickly the eye can resolve changes, rises steeply with temperature. A warm eye can track fast-moving prey in cold water that would leave a cold eye seeing a blur.
The bill's role is less certain than the popular account allows. Swordfish are widely described as slashing through schooling prey, and injured prey with cut marks supports some use of the bill, but the claim that swordfish deliberately impale boats or whales is not supported and collisions are better explained as accidents.