No burning of the core. If you cool it down slowly you're OK.
Pure LN2 is not conductive indeed.
The problem is mobo traces will freeze quicker than the supporting epoxy, thus contracting then cracking.
A solution is total immersion of the motherboard as some crazy ppl did (not for long enough though
)
Another solution is to limit the temp shock, by using some heaters around the core, large amounts of foam, foam pipes to bring LN2 in, a special condenser or at least piping to get gaseous N2 back. You could heat the reverse side of the socket where the pins stick out. Then hello, cryo temps.
Ceramic cpus wont crack/burn. As for new XP's out there, i don't know.
For rich ppl there's also Helium. Expect 4K at phase change and superconductivity states - i wonder how silicon based gates behave in those conditions.