Where's the case?[0] I also don't see the point of lowering the temperature of a plastic battery lid. It's an insulator. I guess it would keep dust off it, though.
(spoilers, and partly replying to your earlier comment above):
It's shown here because part of the storyline requires getting a car. The story specifically has him with a car available, but no battery which he has trouble getting. Just before this scene, he is told there is a car he can use, but of course he opens the bonnet and there is no battery installed (or, it's just the case, I can't remember).
As to why the lid should be in the fridge? My real-world guess is so all the bits are in one place, but the real reason is likely because the audience will more easily recognize the top of a battery over just seeing the chemicals.
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