Hi,
I'm trying to insulate behind my non-venting (it vents indoors) gas
fireplace, as cold air comes through the wall behind it. What kind of
insulation should I be considering so as to avoid melting/fire when
using the fireplace?

Can't see from here, and wouldn't dare to advise, except to contact
local pro for info as to how to seal (sounds like main prob.) and
insulate around it. Failing that, ask mfg. for min. clearances and
other requirements for your unit.

A fire starting inside a wall can burn a house down many hours after
you leave the immediate area.

Insurance companies have a vested interested interest in this sort of
thing, and are understandably interested in fire-marshalls' reports.

HTH,
J