Overheating While Screen Locked
I had similar kind of issue with initial Lollipop version 5.0. I had clean master installed in my phone which showed that nearly 60-70% of RAM and CPU usage even though no apps were running, which end up heating my phone. 

When checked in Settings-->Apps-->Running application mostly were services from android os. But they have now improved it in newer version of lollipop...currently my phone has version 5.1.1. In this it drop from 60-70% to 40% RAM and CPU usage.

Also lollipop has lot of bugs you can find a consolidated list here - https://www.androidpit.com/android-5-0-lollipop-problems-and-solutions