Hill feels Hamilton let emotion get the better of him on occasion last year, which included a number of on-track incidents and his break-up with long-term girlfriend Nicole Scherzinger.
With the new Formula One season just two months away and the slate effectively wiped clean, 1996 world champion Hill believes Hamilton has an opportunity to prove himself.
"What I would like to see from him is that he returns to his roots and comes out at the start of this season showing his very best as a mature driver in the way we know he can be," Hill told Press Association Sport.
"He needs to keep all this other stuff outside of the business.
"Of course, Formula One is a very bewildering place at times for a driver, and with Lewis he has perhaps not had...let's call it a normal upbringing.
"So I can understand him wanting to cut loose a bit, which is fine.
"But when you are in the hotseat in Formula One what people want to see is whether he can deliver and be thoroughly professional in what he is doing when is in the car at the circuit.
"That requires perhaps a little more application than he has been giving it recently.
"There's no doubting Lewis' talent as a driver. It's a question of whether he can find some harmony in his head, and find himself in a comfortable spot.
"Last year he alluded to the way Jenson [Button] was able to be calm, and he slightly envied Jenson's position, the balance in his life, and he is still seeking that."
Hamilton referred to it as "the bubble" around his team-mate that included his father, girlfriend, manager and trainer.
But ahead of a season in which Hamilton ideally could do without any distraction, one of the biggest looms as he is out of contract at the end of the year.
With the prospect of seats being available at Ferrari, Red Bull and Mercedes in 2013, Hamilton could have his pick of teams.
Hill, who is to become an expert summariser for Sky Sports for this season, added: "He has not made it clear where his future lies.
"It may be he will seek to move from McLaren. It may be something he feels he needs to do, which will be a bit like leaving home as he's been there since he was 13.
"So what he does next, that's going to be a big question mark over the season.
"There's no doubt he is an asset as a driver in any team, but there are only certain places where he could fit.
"If I was Bernie [Ecclestone] I would probably want to see Lewis at Red Bull with [Sebastian] Vettel.
"But I can't see them wanting to destabilise themselves because that might be very challenging for both of them, but anything is possible in Formula One."