Why is this the fourth thread on the same subject and why is it in a forum where it specifically says it is for non model specific discussion, instead of being in the Sedici forum?
To try and answer your very fractured question; are you saying that the car cuts out when fully up to temperature, when slowing down and then will only restart after it has cooled down a bit?
The first place I would look at is the crank sensor if your answer is yes. Don't bother with aftermarket replacements, the one I had on my Punto JTD lasted about 10k miles before going bad. Swapped in a genuine one and had no problems for the next 40k until the car was sold. Easy enough to change on a JTD if a little fiddly.