Warm-blooded creatures (mammals and some birds) move heat around their bodies fairly effectively.
Deep-water heat sources set up convection currents that counter the “natural” gradient.
Warm blooded creatures use tricks like evaporative cooling and flow control to move heat around. Some birds, for example, have the veins and arteries in their legs tangled up in such a way that the blood headed toward their feet can give heat back to the cooled blood that’s headed back toward the heart. This prevents a lot of heat loss, but doesn’t actually move heat from low- to high-density regions within the body. Most of the heat involved comes from chemical processes within the cells releasing energy that, ultimately, came from sunlight.
Convection currents distribute heat throughout water by completely normal thermodynamic means: hotter (less dense) water becomes buoyant and rises, displacing cooler (denser) water down toward the heat source. Having moved away from the heat source, the warm water eventually releases the excess heat to the cooler environment and the cycle repeats. Again, there is no heat moving the “wrong” way in those systems.