In his critics’ eyes, DeMarcus Cousins is a locker-room cancer, an elite big man whose volatile ways threaten to sabotage even the most charmed of rosters. But to paint Cousins as a villain, one must brush over a friendlier, more compassionate side of the four-time All-Star.

Therein lies what makes Cousins one of the league’s biggest enigmas: For every person who sees him as a petulant bully, there are plenty of others who know him as a big-hearted 28-year-old who would do anything for someone in need.

In July, when the Warriors signed Cousins to a one-year contract for $5.3 million after every other franchise passed, they banked on getting the latter version. Ask anyone in Golden State’s locker room, and Cousins has been a far cry from the malcontent notorious for run-ins with coaches, teammates, opponents, referees, fans and media members.

In less than two weeks of training camp, as he recovers from a torn left Achilles tendon that should sideline him for the start of the season, Cousins has emerged as a respected mentor and teammate. Those who derided the Warriors for bringing him in might have a tough time reconciling how he has peppered the team’s young centers with pointers, stayed diligent in his rehab and cheered loudly from the sideline in two preseason games.

“People might see him a certain way, but he’s real chill to me,” third-year center Damian Jones said. “He’s been great to have around, honestly.”

When Cousins joined Golden State, he recognized that he needed to do more this season than come back from a potentially career-altering injury or refine his game. His decision to sign with the back-to-back champions was largely about overhauling his reputation.

Entering his eighth NBA season, Cousins is the league’s best player to have never played in a playoff game. His 6½-year run in Sacramento was marked by technical fouls, unflattering sound bites and losing. Though Cousins stayed out of trouble for the most part in New Orleans, the Pelicans tended to play better without him.

Cousins has said that not one franchise offered him a contract during free agency. The reason was simple: In addition to trying to overcome an injury that has derailed many players’ careers, Cousins wasn’t considered the right fit for teams’ culture.

Seemingly out of options, he turned to what he called his “last resort,” phoning Warriors general manager Bob Myers and asking to sign for the mid-level exception. It was a low-risk, high-reward opportunity for Golden State. With four other All-Stars on the roster, it can afford to gamble on Cousins for a year and trust that its system will trump any occasional mood swing from its prized addition.

In Oakland, Cousins has found an environment altogether different from the ones he encountered in Sacramento and New Orleans. Winning is the Warriors’ expectation, not just their goal, and they operate with the self-assuredness that comes with three NBA titles in four years. Instead of criticizing Cousins for his emotional tendencies, they encourage him to embrace his bravado.

“He’s real cool,” second-year center Jordan Bell said. “People paint a picture about him because he yells a lot. He’s just like Draymond (Green). He yells, but he’s a real cool dude.”

One of the biggest questions this preseason is which of the three young big men — Jones, Bell or Kevon Looney — will start at center before Cousins returns. In early practices and games, Cousins has pulled each aside to relay what he sees from the sideline.

During a first-quarter timeout in Golden State’s preseason opener against Minnesota, Cousins reminded Jones to hammer home a dunk whenever he has an open driving lane. Six days later, when Jones snagged an errant lob pass from Kevin Durant and threw it down for a thunderous alley-oop, Cousins, grinning, erupted from his seat along the baseline.

“We’ve been really happy with how he’s been a mentor to the younger guys,” head coach Steve Kerr said of Cousins, who hasn’t spoken to reporters since media day because he is sidelined by an injury. “Whenever they need something, he’s there to help.”

It is a part of Cousins’ personality that some NBA fans overlook. While with Sacramento in fall 2015, he covered the funeral expenses for a slain local high schooler. Two years later, while with the Pelicans, Cousins’ community outreach in Alabama, New Orleans, Sacramento and South Africa earned him the inaugural Offseason NBA Cares Community Assist Award.

It is the great conundrum of Cousins: How could a player with such an unsavory reputation be a hero to so many? Those closest to him reckon that his image problem is the result of being misunderstood. Because Cousins doesn’t trust many people, he feels comfortable discussing his good deeds only with his inner circle.

In coming weeks, as Cousins nears his return to the court, Kerr is intent on continuing to establish a relationship built on trust. Only then can Cousins finally shed his reputation as a locker-room cancer.

“I found a new place where I’m being welcomed with open arms,” Cousins wrote in a recent article for The Players’ Tribune. “... A year from now, looking back, I know this is going to be the best decision I ever made.”

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com Twitter: @Con_Chron