My husband insists on keeping batteries in the refrigerator. Does this have any effect at all on extending their shelf life?
This very topic is addressed here.
I was just looking at battery care instructions from the major manufacturers of batteries, and they all said not to store them in the refrigerator.
“Should I store batteries in the refrigerator?
Storing batteries in refrigerators or freezers is not required or recommended for batteries produced today. In fact, cold temperature storage can harm batteries. To maximize performance and shelf life, store batteries at normal room temperatures with moderate humidity levels.”
from Energizer.com; if they don’t know what’s good for batteries, I give up 
It does have a slight benefit. Batteries are composed of chemicals that will react with each other even when they’re not under load. Lowering the temperature will reduce the speed of this reaction. The difference isn’t huge, but if you’re buying your batteries in bulk and keeping them around for two or three years, you’ll probably see some improvement in shelf life.
Back in the day when I was a part time wedding photographer and used HV flash units, which used a costly 510 Volt drycell, I stored them in the 'fridge between jobs. It seemed to prolong the life of the battery. If I had been working every weekend it probably wouldn’t have mattered, but I only used it once a month or so.
There’s the key. The chemistry in modern batteries is shelf-stable at normal room conditions. Older batteries would self-discharge in a few months, but now, batteries are good for years.
Duracell flat-out says “Do not refrigerate”