How can I build a solar heat catcher around a basement window to help heat the basement in the winter?
I understand the problem of a cold basement. When the ground freezes, a great deal of heat is lost through the basement walls. If possible, I would first dig a trench a few feet down around the basement wall and add solid insulation to the outside wall. Next wrap the insulation with chicken wire and plaster with cement. Then berm the insulation to within 6 inches of your foundation sill plate. These measures will help retain ground heat in the basement.
If you want to add solar heat, a few vertical homemade solar collectors on the south side of your house would help. Solar heated water from the collectors could simply be circulated through a series of plastic drums in the basement. This could at least keep your basement above the freezing mark. You'll need more than a storm window over your window well to add any significant heat to the basement.