If your G4 is running hot it could be because of an actual problem but it's also just as likely to be some app that's gotten corrupted somehow.
-- Go into your Settings >> Storage menu and clear the cached data, and then restart your phone. Those are just the app caches and this doesn't affect any of your saved data. Caches are always just working temp files (i.e. thumbnail pics), apps need them to function but they don't contain anything vital. Since you're already going to restart your phone, you might want to also wipe the system cache partition. See details on that here:
https://www.hardreset.info/devices/lenovo/lenovo-moto-g4/recovery-mode/
Note that Recovery Mode is a text-only interface so you need to use the indicated buttons to navigate through the various menu options. And wiping the system cache partition won't affect any of your saved data. Go through the steps above, select the 'wipe cache partition' option (it will only take a few seconds), and then just restart your G4 normally.
-- If your phone is still running hot after trying the above steps, try restarting your phone into its Safe Mode.
https://support.motorola.com/in/en/solution/ms110838
When in Safe Mode your phone is just running the Android operating system as is, with no third-party apps or services getting auto-launched during the startup process. If your phone is running cooler while in Safe Mode that's an indicator some app you've installed is causing the problem. You'll still need to figure out just which one but it's a lead. Check in your Settings >> Battery menu and see if anything is listed there that looks out of place.
If however your phone is still running too warm while in Safe Mode, than the problem isn't necessarily tied to any user installed app.
-- A last resort option is to do a Factory Reset. It's something of hassle because after doing the Reset you need to restore all the things you did previously when setting up your phone. So it's vital that you make sure you have all your saved data backed up safely. Double-check your backup solution and don't just assume everything you need is safely stored, check it.
Regarding your phone's battery, it's not a user-replaceable one but iFixit has a nice, step-by-step guide on how to do it:
https://www.ifixit.com/Guide/Motorola+Moto+G4+Battery+Replacement/99582
Offhand I don't think it's tied to your overheating issue, but given how long you've had your phone it isn't surprising that it isn't holding a charge like it used to. Smartphone batteries age, that's inevitable,
