Here's a 'grab shot' I took last week of my 2yo nephew contemplating his new paddling pool, using the default Superior Auto mode.
The camera software will be familiar to anyone who has used a recent Sony. In addition to Superior Auto (now with 52 image scenarios in its database) and Manual modes, it comes with the Style Portrait, AR Mask, AR Fun, Face in picture, Sound Photo, Multi camera, AR Effect, Creative Effect, Sweep Panorama, 4K Video, Timeburst Video, and Vine camera apps pre-installed.
The image processing is greatly improved over the Xperia Z; that image is 4.98MB in size (versus the 'native' 20.7MP sensor res) yet there's little loss of fine detail in the foreground grass and background wall. I've yet to experiment with Manual mode, which allows higher resolution capture, and am praying that the 5.1.1 update gives Camera2 API access to RAW mode.
As for overheating under normal use... no. The back of the handset gets slightly warmer, but not worryingly so. I did get an on-screen warning when starting filming 4K video, but I was in direct sun with an ambient temp of 27C and filmed for almost two minutes without problems.