Room has some air leak problem so this would be a good idea for the window curtains. It will help block light in the morning as well. Make Your Own Energy Saving Thermal Curtains HOMESTEAD SURVIVAL SHTF disaster preparedness
DIY Fireplace Cover. Save $$ on utility bills and cover drafty fireplaces. Easily removable. Build wood frame with 1x3s; staple Thermal Window curtain panel over frame; put 1" project foam inside frame (staple if necessary ) and slip over fireplace doors. Fits snug. Lightweight. Easily removed when you want to enjoy fire.
Condensation - Causes and Cures | Thermal Windows, Inc.