It's amazing how many things come with silica gel packets in them. I have a big stash of them in my seed box and tuck them in between the packets. Like others said I think controlling moisture is more important than temperature. Cooler temps are better in general though. An unconditioned garage would have a lot temperature extremes. Plus it's usually not as tightly sealed up as a house and you might have a mouse find your seeds, like I had happen just the other day!
I keep my seed packets in a divided plastic three level storage box meant for Christmas ornaments. I knew I had old photos of it and just went to pull them up from... 2009? Wow, I've gotten my money's worth out of that box! I've changed my organization of it over the years. I used to prepare a lot of packets ahead of time for swaps, guessing what people might want. I don't do that anymore which saves a lot of space and work. Now I use one level for perennials, one for annuals, and one for the veggie garden. I use another shoe box sized box to sort seeds I plant to sow that year based on season and germination requirements.
I've just started to go through and remove a lot of my older seed that I won't likely want to grow again and are too old to swap. I have to make room for more new seeds! I promised myself to never have more long term seed storage than what will fit in the box.