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The IR photons from the cube have much less energy (longer wave length) then the flame. Therefore they cannot make the flames excitation state greater (shorter wavelength). The flame is melting the cube. The cube is cooling the flame. Temperature is the excitation state of atoms. You cannot excite them much more with energy that is significantly less than they already have. Unless of course you split the atoms.

The Earth is the ice cube. The sun is the flame. The sun is heating the Earth. The Earth is cooling the sun. Although it is more or less insignificant. Put some food under an infrared warming light. Is the food making the infrared bulb hotter ?

Put some food under an infrared warming light. Is the food making the infrared bulb hotter ?

Yes, it is, although the warming is very small. The problem is you are applying second law in an open system. Although you might not be applying the second law with "excitation state" theory. Here is a test for the food situation with an open system. Point the IR lamp out into space. Now put the food in front of the lamp. The food absorbs some IR from the lamp, the food warns. We both agree on that. The food emits IR photons. We agree on that. The wavelength of those photons is a spectrum dependent mainly on the temperature of the food:

But the emittance and absorption spectra are the same. Notice that the 500K heat lamp has plenty of overlap with the 300K food. Therefore the food warms the heat lamp a tiny bit. The peak of the food's emission is an order of magnitude weaker than the heat lamp.

This does not invalidate your "excitation state" theory, but that theory must cohere with the fact of the emission spectrum which is measured and depicted above. Your theory also has to cohere with the strongly supported theory (law) that the emission and absorption spectra are the same.

The Earth is cooling the sun

Your mistake is applying conservation of energy to an open system. It only applies to closed systems. If the earth is cooling the sun, then we should be able to remove the earth from the solar system and the sun will get warmer. That is impossible.