The only overheating i got was due to 4K videos and 60fps videos. Camera will shut down after 1mins of each. No loss, the 4K result dont even look as good as 1080p bluray. didnt play any games yet.
My further thoughts, i think the screen response could do some work. i may have a glass screen protector on, but even natively, Z2 has a noticeably higher latency than M8 and S5. Sony will probably get this right with Z3, but one could hope for a firmware update for Z2.
The iauto+ photos are ok as long as you blow them up. i think cellphone photos may come a long way, but still not close to a compact cam like LX7.
The battery is still amazing. spent half a day outside surfing the 'net and taking pictures, and it was still 70%. my pal LG-G2 with kitkat was down to 50%, LG messed up with their kitkat updates to be fair.
the screen colors, really superb. i was a greatest critics of past Xperias' screen, good to know Sony nailed it with Z2....but you will need to tweak the white balance for blues and greens (add about +35 to 40 to them), it will tone down the red hues. reading neogaf dark theme, i think it looks as inky black as my old AMOLED GS2.
Im still not comfortable with the handling. It is a big phone, but not that bigger than S5,M8 and even Note3, but these phones feel safe in my hands. Z2 eats into my palm and i have great fear of someone banging into me. Sony may want to drop the glass back for curved carbon fibre in future phones. So far so good. im happy Z2 is a major upgrade over GS2, i see more people around me moving to Z2 and M8, and S5 sales will not look good this round.