An organism could evolve such a feature, but not for cooling. 50-60 C is not a problematic temperature for organisms, you have thriving organisms at much higher temperatures. On Earth there aren't all that many multicellular organisms at 50-60 C range, but not because the temperature is an issue, but because that temperature range is kinda rare. And is usually found in deserts, so the issue is not temperature but lack of water. If your planet had higher temperatures than Earth, so you had such temperature ranges in places with enough water, multicellular life could prosper. Without the need for cooling. Earth's multicellular life don't particularly like that temperature range because we evolved for cooler temperatures, so our biochemical processes are fine-tuned to different temperatures. If life evolved in greater heat, then those processes would be fine-tuned to those temperatures.
Now your thermoelectric effect could evolve, in hot or cool climate. But not as a mean for cooling, as that is extremely inefficient. An organism would spend way too much energy for it to run the effect full time (which would be needed if it was a cooling mechanism). More energy than it can get from food. BUT! Such an feature would be usable as a weapon/defence mechanism. An extremely hot blade/horn/something could be an effective means of killing your prey. Maybe the prey has protein-based contact toxin on his skin, so the heat (for denaturation of that toxin) was a way to go.
As for biochemistry of this feature: it should be possible. Maybe this organism has some conductive organometals that it uses to generate this effect. Such a thing could evolve in place of nerves; so instead of neuron based control over body this world evolved something that is similar to wires. A tube made out of cells that produce that organometallic and fill the tube, and this transmit electric signals trough the body.