I keep my unopened paper (B&W) in the freezer along with my film. Naturally, a good warm up period is needed before opening to avoid condensation on the paper. I take it out of the freezer at least a day ahead of opening.
Paper does not seem to age as fast as film, as I too have used quite old paper that was stored in normal household conditions. I have some old Unicolor papers that I bought at an old camera shop that are at least 45 years old. They were just on the shelf in the shop, so they saw a wide range of temperatures. They are fogged and not useful for normal prints. I bought them for Lumen prints because I like the results from Unicolor papers. Work great for that.