Share your experience!
Don't do it.
As a former ZL C6503 owner, who now owns a Z C6603.
With the Z being IP certified, IMHO not only does it run hotter than the ZL.
But it also suffers from both a noticeably inferior display, and loudspeaker output, as verified by GSMArena.
Not to mention the headphone jack on the Z is hidden under a flap.
Which I find most annoying?!
It's pleasing to see Sony resolve this with a better solution found in the Z1. :smileywhew:
Be aware that even the Z1 heats up too.
Which highlights when you pack this much processing power with Full HD displays.
Heat is an expected by product when there are no cooling fans, nor heat sinks.
IMHO you're being unrealistic not to expect heat from the current generation of Z series smartphones.
They all do it, to varying degrees. 
.
If your local authorised Sony Mobile service centre has found that both your ZL's performance, and resulting heat output, to be normal, and within specification.
Then what you are experiencing is perfectly normal. 
All the Z series smartphones generate heat to varying degrees.
They are designed this way based on the materials of their construction.
To dissipate heat otherwise the heat will fry the internal components. 
That's why IMHO you will find the Z, with its IP certification, and glass back, will not provide cooler handling than the ZL.
It's for this reason I don't use a case with either my ZL, nor my Z.
To ensure they stay as cool as possible. 
If with same usage "Z" also heats up so much it can also lead to back glass cracking and that is more expensive deal. So forget about "Z". There have been many reports of back glass cracking.
ZL is too slippery without acase. It's almost a similar feeling as holding Xperia P as far as fear of slipping out of hand is concerned.
There's enough information here for you to make an informed decision. 