Yes! It has a fingerprint sensor which sits just below the display. Unlike Samsung phones the home screen button has a built in fingerprint sensor but in Moto G4 Plus, the fingerprint button is just a fingerprint sensor and doesn't act as a home button .
Moto G4 Plus is a great device in this range, it performs decently with great pair of cameras which has Laser auto focus technology, and regular updates from Motorola makes the deal even sweeter. If you ask me the Moto G4 Plus is a combination of both style and power, so it is one of the best phones in this price range.
Heating issues are very common now days the more powerful a phone's hardware the more it heats up. It's just like our PCs the more it works the more it heats up. However it cools down once you close all the apps and keep it on standby mode.