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The problem I have with concluding that the uneven disbursement loses its heat first is simply what was mentioned above, that the warmer temperatures first need to cool to the temperature of the cooler in order to "catch up." I understand that the warmest sections of the uneven distribution...

Further clarification: The bodies are NOT together. Which case (case 1 or case 2) will radiate away all its heat first? I realize the case 1 (nonuniform heat distribution) will have points that radiate heat at the fastest rate (the warmer points) but it will also have points that radiate heat...

I apologize for the omission of said information. I am not an expert in heat radiation so it did not occur to me cover other details. For clarification, I was simply interested in heat radiating away from bodies #1 and #2. Which one would radiate all its heat away first, as in heat bleeding...

No, I'm not a student, though I wish I were, because then I could simply ask my professor. No, my college days are long gone, but the answer to this question is of importance to me. Do you know the answer? Do you know of an easy way to find out the answer?

Given two identical bodies with identical amounts of heat energy, both in a vacuum, radiating their heat away. Body #1 is of non-uniform temperature (let's presume it's hot mostly on one side and cooler on the opposite side) Body #2 is of uniform temperature. Which one will radiate its heat...