I store all mine in the fridge or freezer.
Never bother with setting the temp per se. What ever you keep it at so food does not spoil is fine.

I store lots of seeds in the freezer and fridge and they do fine. The bulk of my seed is stored in 3 large containers in my bedroom closet only because I cannot get them all in the freezer. I like to keep the closet seeds or any seeds in storage at as consistent temp as I can and preferably at 60 degrees F or lower. Easily done in the fridge or freezer.
As to what seeds should not be stored in the fridge I do not know. At one time or another I have stored 40 plus varieties of garden seed in the fridge and they seem to germinate fine.
Straw