Barton, 33, is moving to Rangers on a two-year deal after helping Burnley to promotion to the Premier League.
Warnock, who managed Barton at QPR, believes the intensity of Old Firm clashes against Celtic will surprise the midfielder.
"I don't think even he knows if he will cope with it," he told BBC Sportsound.
"But we saw a very mature Joey Barton last season. No-one expected him to go through a whole season without the red mist descending.
"If he can curb that red mist, it wouldn't surprise me to see him win the player of the season award.
"But I don't know how he will react to the decibel level of an Old Firm match. Now the teams are closer [in quality], and Rangers have already put one over Celtic in the [Scottish] Cup, I see that rivalry becoming more intense."
Last season was the first in five years that Barton was not sent off, but he picked up 10 yellow cards in 40 appearances for Burnley.
The one-cap England international has picked up nine red cards in a 14-year career with Manchester City, Newcastle, QPR, Marseille and Burnley that has also brought 111 yellow cards.
"He wasn't the easiest of players to manage," Warnock admitted. "But if you look at the star quality in players, the top players have that little edge about them. There are not many like Dennis Bergkamp who just have their ability.
"That edge is what makes them a winner. I don't think Burnley would have gone up last season without Joey Barton, and [their manager] Sean Dyche would probably say the same.
"If Joey can curb that red mist, I think he will enjoy it in Scotland more than he has enjoyed his football for many years."
Joey Barton can back up his aim to be the best player in Scottish football if he can control his on-field temper, says his former manager Neil Warnock.