If De Rossi 6 months coaching took Roma to the lime light, and they were able to finish among top four this season, then maybe Roma might decide to keep him to see if he will do better next season. If he is a coach that can study the players very fast, then it will be of a help to him, but if he is the slow type, it will be difficult for him to adapt fast. De Rossi should try and come up with a play pattern that will be able to withstand the strong clubs, so that he will be able to use that as an advantage, if not, it will be difficult for Roma to challenge these clubs. Let's see what he has for the club during this time in Roma. If he is loved by the players, it will be easy for him.
I am sure that if he does very well during this six months, he will be kept as a manager, why would you want to change a manager who can do so much for your club, of course you are going to end up with signing him for longer and longer but I do not believe that will happen. I am not saying it is impossible but he is not the type of manager who had seen so much success, he is not the guy who will make this team top four neither, I do not see that as a possibility.
Roma will continue to do as well as they have done with Mourinho, that is the limit to that team and they will just make it happen that way, the result will not be much different and he will not be really doing anything that would be considered extraordinary at all.