Thank you so much for your kind replies!
Farrusco, that's the cat's name, already sleeps with me. He always has, ever since he came to stay with me, one year ago.
This is what happened: his owner was an old man who died at 97 and his nephew - friend of a friend of mine - promised his uncle he would keep and take care of the cat. When the man died, though, he was unable to keep Farrusco and needed someone to stay with him for a couple of weeks. This was in September and, due to several problems with my friend's friend's house, round Christmas I still had the cat with me! Naturally I had grown very attached to him but I kept my part and let go of the cat when his legitimate owner was ready to welcome him at his new place.
Two weeks later, however, he asked me whether I would not like to have the kitty back. I obviously said yes!
Farrusco had been having a hard time getting used to my friend's other cats (2 youngsters) and was acting all stressed out and aggressive (he's usually very mellow).
When he returned to my house he seemed very happy and I'd even say relieved to be back.
But that's also when the screaming began. I even thought he was replying to the cats outside (it was January, when all the cats are aroused and extremely loud), but perhaps that wasn't the real reason...
Well, I'm sorry to have bothered you with such a long story. Apart from these quirks he's a super cool car.