Insulating small area in attic-like space
One possible solution maybe to construct walls from 2" thick, R-10, foam insulation board. You might be able to make it rigid enough using 3" drywall screws and duct tape. (and perhaps Gorilla glue(?)). If this proves not to be strong enough, you can use some cheap strip furring to add strength.  R-10 will certainly not be sufficient if your low outside temps drop and remain in the 20s or worse.

The foam board is NOT cheap however. It'll probably cost you around $250-300 for that (10 sheets 4x8 @ ~$25-30ea.). You might can even use one of the sheets as a door--with duct tape 'hinges'. (if that doesn't work well, you can just fashion some handles to it and remove/replace as a door entry way.).

It you are running computer equipment in the area, that will reduce your heating needs if you leave the equipment running. Good luck.