Hi,
You want to keep your seeds cool, dark, and dry. Your closet is a better place than the garage probably. The reason being dry is the most important of the three. Moisture/humidity is a sure way to lessen seed viability. The second is temperature swings in the garage. It better to have a steady temp.
So though the garage may be cooler at times, the humidity and temperature are not as regulated as in your home.
Remy

Then would a criper in a fridge, plastic zip locks in a light tight box, be OK? Been keeping in Ziplocks in a shoebox.

It depends on the fridge and the container. You need to keep the seeds completely dry. So the outer container must be completely sealed and airtight before putting in the fridge. Any moisture that might sneak in is bad. Personally, my fridge is way too moist. I would not chance it. If you are not removing seeds only once or twice a year, and can ensure a good seal on your container, then it is ok. If you are trading seeds, then I recommend storing them at room temperature because of the temperature swings of taking them in and out of the fridge, and again chances of moisture possibly getting it.
Most seeds kept at room temp and dry will last for at least 5 years before losing some germination. A few like onions will deteriorate quicker and some will last longer than 5 years, but most do well for about 5 years.
Remy

The long term seed storage vault in a mine in Norway is described as "The seeds are sealed inside 4-ply envelopes, and then placed into plastic storage containers. From there, the storage containers are placed into seed vaults. The mountain interior itself stays at a constant âÂÂ3C (27F) temperature."

Yes, if you want to have very long term storage, freezing is the way to go. You have to be careful with freezing though or you can kill all your seeds.
First, they must be completely dry. So after saving seeds, they must be left out for some time to enure there is no residual moisture. Beans can be tasted with a hammer on hard surface like a driveway. If they smush, they are not dry enough yet. They need to shatter.
Second, they must be put into a tight sealing container
like a canning jar.
Lastly, you must let the container come to room temp before opening the container or you will kill the seeds.
If you are only getting you seeds once or twice a year, this can be an option, but if you are getting seeds more often especially with trading, I don't recommend it. Again because things can go wrong and temperature swings are not good for the seeds.
Remy

Apart from condensation, is there any other reason why temperature swings should be a concern? What if the temperature swings are only between freezing (without actually freezing) and room temp? Is freezing/thawing even a concern if the seeds are plenty dry?

I find this to be an interesting thread. Have been keeping my seeds in the small downstairs freezer (about -5F). I throw in a dry pack or two if any are available.

May have to re-access my method. There are some sites giving seed expected lifetime, but not much info on how to store them.