Vryjdfkk

Suppose I take a group of alligators select the ones that emit the highest frequency of radiation (since all living creatures emit thermal radiation), and I breed those, and get rid of the rest and continue this for thousands of generations. Is it possible, that at one point the frequency of that radiation becomes high enough to enter the visible light spectrum?

My theory is that, since the criteria we have selected for the selective breeding is high frequency radiation, a point should come where the radiation becomes high enough for us to see, because after all, it is the body that is creating the energy, which depends on the genes of the alligators.

And if it is possible, could we exceed the visible light spectrum? Maybe reach a point where the alligators start emitting X-Rays or Gamma Rays? And do you think the alligators, as creatures, would completely change in order to keep up with the selective breeding system?

EDIT:

After seeing the answer's I've got, I remembered that alligators are cold-blooded, so would this work for warm blooded animals like monkeys, or any animal if possible?

No, it doesn't work that way.

I select the ones that emit the highest frequency of radiation (since all living creatures emit thermal radiation)

Black body radiation is emitted by anything above the temperature of 0 K. Alligators, being cold blooded animals, are just at the same temperature of their environment. There is no thing such a hotter or colder alligator, you would basically pick some based on the local environmental temperature (i.e. sunlight or shade).

Is it possible, that at one point the frequency of that radiation becomes high enough to enter the visible light spectrum? Could we exceed the visible light spectrum? Maybe reach a point where the alligators start emitting X-Rays or Gamma Rays?

Different wavelengths are emitted as a consequence of different transitions.

Low frequency electromagnetic radiations are emitted by electron oscillations, while visible light up to X ray is emitted by electronic transitions within atoms. Gamma rays are emitted by transitions within the atomic nucleus.

Moreover, radiation with energy comparable to UV and above is dangerous for living being, as it usually damages the organic molecules.

In order for a body to emit visible light as a result of black body radiation, that body has to be heated up to close to 620 degrees Celsius, or 1160 Fahrenheit. Think of light bulbs.

Your gators can only reach that temperature with human intervention involving fuel, and they won't be alive for most of the time they are that hot.

Fireflies emit visible light not through black body radiation, but as a result of luciferin reacting with luciferase in their bodies. It could take hundreds of millions of years for alligators to accumulate enough random mutations for that, but you could speed up the process with genetic engineering.

No. Not in the way you are suggesting, and not to the frequencies and power that you are dreaming of.

However... you could go around your problem and have a symbiotic relationship with some light emitting animal (e.g. a firefly), or bioluminescent fungus, or bacterium (as in the case of a certain squid).

You would "only" need to create a selective pressure for the two organisms to cooperate. In the case of the squid, the cephalopod needs to camouflage by imitating the brightness of the sea surface, and the bacteria are just happy to be carried around. In the case of your alligator, the light could attract some nocturnal preys, or camouflage the alligator during full-moons. The bioluminescent animals could benefit from cleaning the dirty teeth of the alligator, or cleanse its skin from parasites and ticks, or simply enjoy being carried around for the sake of it.