Most lumber yards carry Styrofoam insulation in 4x8 foot sheets. You want the 3/4 thickness. Line the inside of the room with that and it will be much easier to maintain a stable temperature. Styrofoam will burn, so you have to cover it with paneling.
While you are at it, count all the electrical outlets and switches on outside walls and get insulators for those. You take off the plastic plate an insert the insulator under it. Look carefully around doors and windows for cracks and either tape or glue them shut. If there is any space beneath a door when it is shut you can get a fabric snake to fill that gap, or go back to the lumber yard and ask for a door sweep.