Why should this be forbidden?
There are no moving parts inside the Unit (like HardDisks or something).
The only thing i would avoid is frontplate facing the floor, that would be very impractical 
Jokes aside... I don´t think that this is permitted in any way.
I'm sure it'd work but i'd be reticent to do this for fear of cables falling out of the back.
As i experienced, the cables lock very tight in their connectors. So they won´t come out at any position.
Do they get very warm after a few hours of being on?
No, they remain cool.
I mean it, they don't get hot.
I run mine this way all the time...both the unit I had previously and my new one. No issues. For some extra measure of safety, I use a 90 degree neutrik end on the input from the cable and I pull the cable back and velcro tie it to the side of my rack case so that I don't accidentally pull it our or bend it.
Mine fell off the back of a stage once and landed on its back (somehow I didn't throw up in my mic after watching it fall), finished the set and it's like it never happened. Didn't notice any tone improvement while it was vertical.
One day people may speak of the original 'Vintage' Kempers, complete with 'dings and dents' making them 'Authentic Vintage', by definition they will of course sound better than those which are to follow.
Log-in in 30 years time to read the threads! 
