[KVFinn]

This is what I use now. After leaving them plugged for years the batteries often start expanding though, so it's not ideal right next to my head all night...

[MayeulC]

You need a charging controller that can disconnect the battery. IIRC my Xperia T3 was capable of that.

On Android, Advanced Charging Controller App (AccA) can tell you that, and help define profiles to avoid that spicy pillow issue.

Some phones additionally support running without battery, or you can connect a power supply in place of the battery.