You could also use store. "Store" suggests to me that they have a supply of batteries, and that they store them over a length of time. "Keep" is a less suggestive term (to me). It simply tells me that they put their batteries in the fridge, and that's where you'll find them. In this case, the difference isn't really significant.
Edit: As usual, I was slow, and two responses above were posted while I was writing this.
I don't remember exactly why I'm suspicious about "keep".
Sometimes I think I can use a verb in a certain way, and I can't.
The other day I used "maintain" and a native speaker couldn't understand me.
There is a machine.
In this machine, there is the part "A".
The guy makes a change in the machine and part "A" seems to me not to be necessary anymore.
Then I ask him "why did you maintain part A" and he doesn't understand me.
He replies me "are you asking me why do I have to have part A?".
"Maintain" and Portuguese "manter' look similar and mean exactly the same, but just in the dictionary, I think.
Is this case, could I have used "keep"?
Yes, indeed, you could use keep. You would be understood to be asking, "Why do you have it here instead of getting rid of it." We would understand "Why do you maintain ...?" to be asking "Why do you repair this and do what is necessary to keep it in good working order?" (I tried to avoid using keep here, but couldn't.)
Your post looked like it was going off-topic, but then you brought it around to your original question. Nicely done. .