If the manual says to not use lithium - then don't use lithium.
You can use rechargeable NiMH AA batteries.
They will last about three to four times longer (on a charge) than Alkaline batteries last.
That makes them more cost effective to use, because you can recharge them.
NiMH batteries/charger kits are available at all stores that sell digital cameras.
..
The manual says not to use them in this camera due to possible heat, but it would sure help battery life if I could. Has anyone had problems doing this?

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