The least expensive insulated battery box will be an ice chest (plastic) not
styrofoam. Use 1/2" plastic water pipe for vent. Vent it to the outside of
the building, as straight up as possible. Avoid 90 degree bends if you can.
The vent should be at the highest point possible inside the box. You want
a chimney effect. Seal the plastic pipe with PVC cement so it can't come
loose or be knocked down.
The inlet should be screened and at a low point in the box. Preferably,
vent on one end, inlet on the other. Large ice chests usually have a drain,
so use it as the inlet. Since the air in the basement is never below
freezing, you should have no worries. If you are concerned, put a small
solar panel on the roof. It will keep the batteries warm and prevent
self-discharge.
I'm not sure what you meant about not getting any charge retention.
How old are the batteries?
How long do they sit unattended at a time??
Is there any drain on them while you are not there??
How often do you clean the tops and terminals??
What is the coldest outside temperature during the winter???
"mountain location which is quite cold in the winter"
I live in the mountains, and 20 below is not unusual, sometimes
30 below. So the term quite cold is relative. (At least that's how my
relatives act towards me.)
Ralph