"They know it wasn't really my choice," Cole said with a smile Monday.
Cole was in Miami for an introductory visit after being drafted 28th overall Thursday night, then traded by Minnesota to the Heat for the rights to guard Bojan Bogdanovic, a second-round pick in 2014 and cash.
Cleveland fans have been rooting against the Heat ever since LeBron James chose them over the Cavaliers last summer, but Cole said his new team's unpopularity back in Ohio doesn't bother him.
"I've liked the Heat anyway," he said. "I was cheering for them. Some people didn't like the fact I was cheering for them, but they're happy for me and my success. Some people have bad comments to say about LeBron, but I ignore them."
He'll meet the trio eventually, but perhaps not for a while. With the NBA's collective bargaining agreement set to expire Thursday, a lockout looms, which could mean the postponement of summer sessions designed to speed the development of rookies.
Cole said he'll work out in the Midwest while waiting out the labor dispute.
"I'm going to control what I can control, and that's getting better on the court," he said. "When I get the call saying I can be back down here, I'm going to be back down here."
Heat president Pat Riley chuckled while acknowledging his reputation for being wary of relying on rookies like Cole.
"That's not true," Riley said. "If he's a player who can play, he's going to be on the court. We can't wait to get started working with Norris."
Riley said Cole possesses the speed to change the pace of a game, which may lead the Heat to play a more uptempo style next season.
As a senior Cole averaged 21.7 points, 5.8 rebounds and 5.3 assists for a team that finished with a 27-9 record. As a sophomore he scored 22 points to lead the Vikings past 12th-ranked Wake Forest in the first round of the NCAA tournament on the Heat's home court.
He was watching the draft at home in Dayton with 80 friends and relatives when he learned he was heading back to Miami.
"We were all gathered around watching TV," he said. "When everyone heard my name called, it went crazy and the house started shaking. It was a great feeling."
As for what kind of support Cole will get from Clevelanders now that he's with Miami, he makes no predictions.
"If they want to cheer for us, that's fine," he said. "If not, that's fine."