With sore legs but unflinching determination, the most scrutinized athlete in professional sports stands on the cusp of finishing off one of the most remarkable postseasons in NBA history, hoisting the championship trophy for the first time and silencing critics who wondered whether he had it in him.

With one more win, LeBron James not only will lift the Miami Heat to its second title in franchise history, but also complete the triumphant transformation from NBA Finals scapegoat to playoff hero.

“I have a job to do, and my job is not done,” James said Wednesday, on the eve of Game 5 of the NBA Finals, with the Heat leading the Oklahoma City Thunder 3-1 in the best-of-seven series.

But James might enter Game 5 at AmericanAirlines Arena with some degree of discomfort in his legs. He left Game 4 twice because of cramps, forcing him to miss 2:05 of the fourth quarter, including the final 55 seconds.

“I should be fine by [Thursday] night,” said James, who took jump shots and participated in the Heat’s light walk-through practice on Wednesday. “I’m still sore. I feel a lot better than I did last night.”

While nobody can say for sure if James will be 100 percent, athletes typically recover quickly from cramps and the Heat is optimistic it will be a nonissue in Game 5. “We’ll be able to better hydrate and be more proactive now,” coach Erik Spoelstra said. “He feels better and hopefully by [Thursday], he will feel ever better.’’

Even with the cramps, James returned to the court to hit a three-point shot that broke a tie with 2:51 left. The Heat never trailed again.

That was the latest in a string of sterling moments for James in this postseason — a stark contrast to last year’s Finals loss to the Dallas Mavericks, when James was blasted for being passive and unproductive in the fourth quarter of games.

James admitted Wednesday that he was “very immature’’ in handling the aftermath of that series.

In these Finals, James is averaging more points than last year’s Finals (29.3 to 17.8) and grabbing more rebounds (10.0 to 7.2). In Game 4, he became the first player to produce 26 points, 12 assists and nine rebounds in an NBA Finals game since Larry Bird in 1986.

“Once LeBron wins a championship, he will go down as one of the 10 best players ever,” TNT analyst Charles Barkley said. “We have never had a guy [like him] that is physically gifted that can run and do everything. He covers up a lot of their flaws. It’s an honor to watch him play.’’

Most significantly, he is making more meaningful plays in the moments that matter most.

“Like I said before the series started, I wanted to make game-changing plays because that’s who I am, and that’s what separates me from a lot of players,” he said Wednesday. “Plays that seem out of reach, I try to make those plays. I didn’t do that last year in the Finals, and that’s what stuck with me more than anything.”

James, in the past few months, has spoken of becoming a recluse after last year’s Finals, staying in his home for two weeks, trying to shield himself from the venom of the critics laughing at his failure.

“I was very immature,” he said of his reaction to losing in the 2011 Finals. “I was very frustrated, very hurt that I let teammates down. Last year, I played to prove people wrong instead of just playing my game, instead of going out and having fun and playing a game that I grew up loving and why I fell in love with the game. I was very immature last year after Game 6 towards [reporters] and towards everyone that was watching.”