Do capacitors have the same problem? I know they’d take longer to charge than discharge, but I don’t know temperature requirements.

Capacitors are blindingly fast in both charging and discharging compared to chemical batteries, and are much less susceptible to thermal variance in performance to boot. Their downsides are greater mechanical fragility, greater self-discharge, and comparatively terrible energy density.

I believe it would depend on the type of capacitor. A metal foil capacitor would have no problem, but an electrolytic might. The rate for capacitors is so much larger than batteries I doubt it's actually a problem.