Since your description is a bit generic, here are some generic ideas (terms) that you may want to take a look.
- patching compound
- putty knife
- drywall repair kit
- foam strip adhesive
- caulk
- expanding foam
When I was college I bought two big pieces of plexiglass and mounted them on the inside to cover 2 of the windows in my room.. That was mostly for noise reduction, but it should help with draft, too.
And BTW, if you leave them on long enough, most 'non-residue' masking tape will leave some residue, and it might be difficult to remove them if they are left on long enough. Don't ask me how do I know that. đ
Their intended usage is masking for painting, and it's expected that they'll be removed in no more than a few days, if that much.