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.
Here is an easier example. Take three metal rods being warmed by constant independent sources. You have a metal rod warmed to 80 C in a room at 30 C. You take two other metal rods warmed to 50 C and connect them to the 80 C metal rod. That will not increase the temperature of the 80 C metal rod. It will decrease the temperature of the 80 C rod and increase the Temperature of the 50 C rods. Exactly as the flame and ice cube example. Or exactly as the Sun and Earth example. Energy flows from warm to cold. Always. From high excitation to lower excitation. Not the other way. Used to think it could, but have recently been convinced it cannot.