It is hot because that's how Li-ion behaves when charged. But unless it is much hotter than a smartphone after some very intensive 3D gameplay, there is really no real concern there.
Get the biggest current output USB adapter you can find, but even a 0.5A adapter will work just fine (except for a longer charging time). One thing to note is that the really cheap eBay charger might burn-out when it is over-drawed (because of the lack of protection circuit inside) - but that's not limited to charging X5 and can happen to charging any demanding USB devices.
From what I learned about Lithium Ion batteries I was given the following direction. Once my tools or devices with Lithium Ion batteries runs out of juice, DO NOT CHARGE THEM RIGHT AWAY. Let them cool off for 1-2 hours before you charge them. The life of the battery will be reduced and the capacity can be affected if you do not do so.
Not sure if it's snake oil or not but read it in two places and do this with my power tools. I don't want to shorten battery life and definitely not charging and playing at the same time on this lovely device.