Wild camping in Italy is often forbidden. But just sleeping in your car or trailer for one night in a parking space with the purpose of recuperation is exempt from this (with good reason, you prefer people stopping to sleep to having them risk accidents). 
But I would be travelling by bicycle: Is it legal to stop for less than 12 hours at a place, just put an isolation mattress on the ground (and a bivouac sack if it rains) and sleep there next to my bicycle? Are there conditions on it?
I'm aware this carries certain risks from criminals, but I wouldn't leave my stuff alone, ever and I would be surprised if someone was willing to actually fight me for my battered trekking bike and other heavily used but high quality gear or the amount of emergency money I would need to carry (no expensive watch, smartphone, camera and the like which are likely easy to sell). If you think I'm wrong, then feel free to make this part of your answer, otherwise keep it to the legal aspects.
I suspect I would hardly be fined for this, but I would like to know about the law.
On the motivation for my question: I would like to go to my limits concerning to distance traveled per day. This means that it's impossible to plan my stops ahead of time. The quality of roads influences my speed a lot, weather too and of course I don't always perform the same way either. I would expect to do anything between 100km and 250km a day depending on circumstances.
Because I don't handle heat too well (or is this just general good sense?), I would start very early in the morning, take a long break including a nap around noon and then continue very late into the evening.
So neither hotels nor campings nor anything of the like is really practical, even if I'm willing to pay for it.
Edit: Done this a couple of times now. To be one the safe side, I just made sure no one saw me... And I usually stopped 10-12pm and started before 6am, so I was never at a single place for long.