Hey Bruce, not sure the 100% best answer to your battery question, but for tool batteries and lithium in general I believe the medium-heat theory applies - keeping things in the middle.
Room temperature at about 50% charge - best NOT to store in extremes(too hot/too cold) & (zero/100% charge) so an insulated garage on handy shelves is what I've seen. There's inspiration of people making custom built in or bought storage solutions.
Plumber:
I have a contact from Tom Drexler who did good work for me that I'd recommend:
KevinC