I'm pretty sure a refrigerator would work if you put the wet clay under vacuum with a valve that would close to recharge it.
Discussion
Depends on your cold side temp.
I was thinking the opposite direction. That we could reuse a lot of readily available apparatus to make cooling out of miner heat if the temp for the ammonia conversion was lower.
When I saw it didn't work I figured I'd post anyway to save anyone else with the same thought the hassle of looking up that temperature.