The unique cracked box - specially constructed for this episode - was recently sold in Propstore/BBC's November auction for Children in Need, along with Astrid Peth's costume from Voyage of the Damned. The winning bid on the box was £11,000. You can find the auction page here.
Several photos were included on the auction, including a rare roofless top-down view. However, due to the box's unique construction requirements (full internal lighting meaning there was no need to 'pretty up' the inside), I don't know that a common construction method could be extrapolated from it.
I'm trying to work out what the box is made of. The inside looks like a low-density plasticky material with the absolute minimum of plywood to hold it square. It definitely looks like they went all over the outside with something like a soldering iron to get all those melted lines, and it totally read as cracks on-screen.
Love the simple solution of massive amber lighting gels for the fiery glow.