Nooooooooooooooo, don't put it in a fridge, cold of any sort is not good for yeast. Yeast is a bacteria, which means it is just as vulnerable to extreme temperatures as you and me. If you leave it in a snug cupboard it should be just fine.
Wow. Just... wow. Others have said it already, but pay no mind to this nattering ninny.
Let's just go bit by bit here for full effect:
1) "cold of any sort is not good for yeast" - Quite the interesting commentary since yeast is stored at -80 degrees Celsius in lab settings as the preferred and really "only" way of storing it long term, although they do take precaution to keep the cells from rupturing as they reach sub-freezing temps.
2) "Yeast is a bacteria" - Absolutely incorrect. Yeast are Eukaryotic cells (meaning their DNA is contained within a nucleus) and bacteria are Prokaryotic cells (no nucleus and DNA is effectively uncontained within the cell). In fact, the difference between them is so stark that it is defined at the very first tier of classification beneath basic life (Life-Domain-Kingdom-Phylum-yadda-yadda). Prokaryotes encompasses bacteria, viruses, etc, and has nothing to do with yeast, while the domain of Eukaryotes encompasses literally every other living organism above the Prokaryotic level. Humans diverge from yeast at the next basic level as being under the Kingdom of Anamalia while yeast are under the Kingdom of Fungi. But hey, details shmetails.
3) " which means it is just as vulnerable to extreme temperatures as you and me" - Yet another hilariously incorrect statement. Bacteria are highly evolutionary (a concept the poster here may not believe in given their lack of very basic scientific understanding) and different strains have been found to exist and even thrive from freezing all the way up to 200 degrees F... a temp "you and me" can't survive in...
4) " If you leave it in a snug cupboard it should be just fine." I guess we can let this one slide since we can leave "just fine" up to interpretation