Probably, due to faulty insulation/damp barrier, there is a cold draft coming through one of the upstairs baseboard. What is a good method to seal it? (It is a rented house, so, no I do not want to fix the source of the problem)
If the gap isn't too big, regular caulk will seal the gap between it and the wall. If you're using it at the top of the baseboard and can get it in the same color as the baseboard, you might not even have to paint it.
Spray foam maybe? They sell it at local stores here, I believe it's called "Great Stuff". You spray it in cracks and it expands to fill the gap.