Frost forming in basement corner.
frost, of course, does not form where it is warm, so i think you've answered your own question; insulate! i feel that the best insulation for basements is on the outside, and rigid foam; lots of it if you are in a cold zone. that is going to require flashing over the top of it and under your siding, if they are in the same plane, which is a pita, but necessary. you can insulate w/ rigid inside, too or instead, but make absolutely certain that there is no air going to run around the foam and hit that cold wall. if it does, you'll still have frost there. the hairline cracks? seal from the outside, if at all possible. they could be letting cold air in, if not water when it is warm. do a search here for "insulating basement" and you'll have plenty to read for a while. good luck.