Not turning on after nand replacement

What were the phones symptoms before replacing the NAND?

By "NAND replacement", do you mean that you desoldered the flash chip and replaced it? I'm not discounting the fact that it's possible to do this, but there are a few possible issues I see here. Aside from the possibility of a short or cold joint (without xray you won't be able to verify this), there are a few other potential issues I see with this. If you aren't using the correct replacement part, or orient it incorrectly this could cause problems. If the phone didn't work before, it's possible the NAND wasn't the problem to begin with. I'm also pretty sure that the iPhone NAND is encrypted with a key unique to that iPhone, and if you replace the chip with one from another phone (or a blank chip) the phone will fail to decrypt the flash and not even begin the process of booting. The fact that its getting really hot would be indicative of a short. Even if you're verifying no-short by probing power rails on the logic board, there are several different power rails and one of the other ones could be shorted out.

@imicrosoldering @chrisgreen If someone needs to come on iFixit to ask why the phone overheats and doesn't turn on after a Nand replacement, I believe the answer is already in the question itself ;)