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It already exists. There is a company that sells a space heater that mines crypto currency. You get like 50% or the profits which sucks, but you at least recoup a bit of the cost of the electricity to run the heater.
I think we should try to heat ourselves with computing as much as we can since the side effect of computing is heat generation (and minor RF losses). How cool would it be to make a large supercomputer out of millions of homes heating up in the winter?
People suggested formatting to exFAT which is valid, but first you could just try either compressing the file (tar czvf file tarball.tgz for instance). FAT32 cannot handle files larger than 4GB, and compression might just make your file small enough.
As a workaround you could also split it in half and stich it back on the target machine