Xperia Z5 Compact overheating

[Xparc]

I have previously had an Xperia Arc, which had too many flaws to even mention here, but my new Xperia Z5 Compact shares one trait with my old phone, which is the overheating issue. I set up my phone on Sunday, and it began overheating immediately. It hurts to touch the back of the phone, and the screen is uncomfortably hot to touch. Is my phone faulty, or is this a common issue with this model? I always set the screen settings to the lowest brightness, I always turn off any image enhancing setting, and I never use adaptive brightness. I have had a Nexus 4 before I went back to Xperia, and I am aware that certain apps and usage will cause a phone to heat up. My concern is that I have used this phone for less than a week and I immediately encountered an overheating issue without heavy usage, and I can't keep a phone that hurts my face if I make a phone call. If a phone hurts to touch, there's usually something wrong.
Is this a common issue?

[Bhonder]

My Z5c was very hot during to first days. Let some battery cycles and all will go fine.

Mine took a week or so to settle down.

Sometimes it heats but only for a while.

[Xparc]

So if it doesn't get better, then there's probably something wrong with it?
Thank you for responding

[Bhonder]

To tell the truth, my Z5C took a month to behave but now it is fine. During the first days a lot of heat comes from the battery break in. Anyway there are many indexing services (like photos, for example) and other running in the background.

If you are one of those user with a lot of "social" apps and the mail in push mode all day long, then you have to expect that the phone is often busy, hence warm.