Personally, I think you are 100% right to just keep them in a place they can get air (inside those paper envelopes is fine I think) and leave them at room temp. Believe it or not, this very year I planted some seeds that had been in the same type envelope for 4 years. FOUR YEARS. Germination rates were MAYBE 10% less than fresh seeds. The vast majority sprouted and grew and fed lots of coyotes! ha.
I think you were asking only about storage of purchased seeds, but for anyone interested in saving their own seeds:
When I save my own seeds, I wash them off just a little (I find that washing too much DOES hurt germination…I actually have better luck when the seeds I save stay a little bit sticky for a month or two. Eventually the stickiness goes away, either from dust or further drying. But many people try to wash melon seeds to they are not sticky when they dry an hour or two later. The thinking is that the stickiness will hold moisture or create it or something…but I definitely notice a marked improvement by just barley washing and laying aside so that once dry they are sticky for a while. After I gently rinse them off, I spread them out on newspaper. This also seems to work really well- better than laying them on a non-porous surface like a plate or counter top. With those hard, non porous surface I find the top of the seed dries faster than the bottom and the bottom holds moisture too long. Also, on larger seeds, believe it or not, if you lay them on a nonporous surface where the top dries before the bottom, the big seeds will actually curl a little bit! It isn’t dramatic or very noticeable and I can’t say for certain it hurts germination rates, but you know it can’t help and it worries me so I use newspaper, paper towels, etc. I let them dry like that for 2-3 weeks. Then, and really this is mostly just because I need the space (it takes a lot of space to spread seeds out on newspaper so that none of them touch) I will combine them onto a paper plate (the cheap, uncoated ones). At this point I will put them on the paper plate touching- in a small pile. But they can still breath. I leave them like that for a while longer (between 3 weeks and next planting time in spring). Then they go in…paper envelopes! So ultimately I store my saved seeds just like you are storing the ones you bought.
On a side note, some people reading this may not have seen my extensive posts about how even though I grow many different varieties within 15 feet of each other I don’t see any obvious crossing. @fruitnut has done a great job of pointing out that biology and the rules of nature tells us that my melons pretty much HAVE to be crossing, and I know its true. I can only tell you that in the extensive years I’ve been growing melons and saving seeds, I just haven’t seen any (well, maybe a few questionable cases) obvious crosses. Again, I understand it must be happening, I can only say that I’ve not seen any/many melons that don’t look just like the one the seed came out of. I throw that in for any reader who might ask me if seed saving results in franken-melons. ha. I haven’t seen it, but I’m sure genetic testing would prove it is happening.
ONE LAST WARNING ABOUT SAVING SEEDS OR STORING WATERMELON SEEDS!!! This applies to your seeds, to, @Matt_in_Maryland ! NO MATTER WHERE YOU PUT THEM…WATCH OUT FOR MICE!!! THEY LOVE LOVE LOVE watermelons seeds!!! Last year, I put 2 paper plates full of seeds on a dresser in my spare bedroom.I rarely go into. I put those plates full of seeds in there last Nov and when I went in the room about a month later, one plate had a grand total of 5 seeds on it (it had probably 200 when I put it there). Those 5 were empty or rotten…gota give the mice credit for only taking the good ones. haha. The funny part of this? I saw no chewed up seed bits anywhere and was perplexed by that. In the past when I’d seed mice eat watermelon seeds they would chew the seed open, somehow pluck out the inner kernel, and leave the outer part alone. But this time they just cleaned out the whole plate and left no scraps. About a week later I retrieved a pair of shoes I had stored in that room…opposite side of room, probably 18 feet from the seeds. And yes, you guessed it, I pick up the shoe and find about 250 watermelons seeds!!! hahaha. I mean that shoe was absolutely packed from toe to heal…probably 3 cups of seeds. AMAZING. I almost felt bad for taking all their fall work and stores. Funny I felt bad for that but not for setting a trap to KILL them! haha
Moral of this, a ridiculously long post even for me, is to leave all seeds at room temp where they can “breath” and watch out for mice.
Oh. I agree with @bchiker about storing them in a freezer. I know lots of people do that, but I have tried it more than once and am certain that it reduces the germination rates - at least for me and my way of doing things. I know lots of people do it, but I just can’t recommend it. The old man across from me puts his in a jar and then in freezer. I think BOTH of those things are bad for seeds, but he does it and gets pretty good sprout rates (but I always notice he has several hills that don’t come up and must be replanted).
Hope this helps someone. To the others I’m sorry you had to read all this! ha