I have a battery-powered hedge trimmer with a lithium-ion battery. Is it safe to store inside?

I only have my house, no shed outside or any other outbuildings. I do have a storage box thing on my patio that I keep gas cans in, but it's not that far from the house... It also really doesn't protect from the elements like hot and cold, just rain and such.

Anyway, I've now seen two videos of lithium-ion battery fires, and this is freaking me out. I clearly can't just leave the battery outside, but now I'm worried about leaving it in my house. It is unplugged when not charging before use and especially when I'm not home, but I've heard of them exploding, even when the battery has little to no charge and hasn't been used in a significant amount of time.

I know next to nothing about these batteries or technology, so bear with me here.

My dustbuster thing also has a lithium battery, and I've just unplugged it. I'm sure my cordless Shark vacuum probably does as well.

Should I be worried about any of this? What should I do if storing the hedge trimmers in my garage is not a good plan?