I have a bath room in a barn at farm with insulation temp gets to about 40 most winter .I don’t turn heat on till it gets below 20 outside then keep it at about 40. In the summer it will get to 80 or so. So would ammo be ok in cans in there ,would like to get it out of house.
Throw some of those moisture absorbing silica desiccant packets in the ammo cans for some added protection. If you don't have extra they're pretty cheap online
Sounds like they'll be fine as long as the rubber seals on your cans are solid. I moved here from a much more hot and humid climate and stored a lot of my ammo in a shed. Relied on quality ammo cans and a bunch of these silica packs from eBay and never had a problem with the ammo.
I bought some some silica beads in bulk and a pack of disposable drawstring bags used for loose leaf tea. Way cheaper per bag and I can throw a bunch of bags in each can.
I just discovered 30 (+/-) rounds of 22LR loose in a pouch, left in the unheated barn for at least a couple years..the lead was turning white, some brass had verdigris on them. All but one fired first time.
Ammo is pretty tolerant if it's kept out of hi humidity environments
I have mauser ammo stored in ammo cans that dates from the 1920's and it all has gone boom just fine, i have 7.62x51 that was in cardboard packages took it out as the paper was causing issues with brass getting green junk on it. most of it was south african made in 81 and in the plastic battle pacs too.