H2O2 decomposes to a final product of H2O and O2, but if you look at the initial chemistry it first undergoes free radical formation. Put extremely reactive free radicals in your cooling loop and you will rapidly have a Cu(0) to Cu2+ transformation. This probably occurs to some extent anyway eventually, but a thick layer of Cu(II)(OH)2 in the block (Cu2+ + 2 OH- -> Cu(OH)2(s) will impede heat transfer and will be difficult (impossible?) to clean.
Summation? Bad idea.
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