CKE Restaurants chief executive Andy Puzder is known for doing things his own way. When a health-food kick hit the fast-food industry a few years ago, the head of the Hardee’s and Carl’s Jr. hamburger chains went the other direction.

“Everyone was doing salads and applesauce. We said the hell with that. We’re going to do Monster Thickburgers. We’re going to put Paris Hilton in a commercial,” Puzder told the St. Louis Business Journal in 2009.

But now that Boston private equity firm Thomas H. Lee Partners plans to buy publicly traded CKE for $928 million, employees, investors, and analysts will be watching to see if changes are in store for Puzder.

Puzder has a lot riding on the takeover. He owns 1,366,852 shares of CKE stock, according to his latest SEC disclosure made February 9. His stake is worth $15.1 million, based on THL’s proposed acquisition price of $11.05 a share.

Puzder is also one of the highest-paid executives in the fast-food business and earned a $7.4 million pay package in 2008. By comparison, Jim Skinner, CEO of McDonald’s, the world’s largest fast-food chain, received $13.6 million in 2008. With 32,000 locations, McDonald’s is more than 10 times the size of CKE, which has 3,100 locations.

It remains to be seen, however, whether Puzder and CKE’s new owners will see eye to eye.

THL, which took Dunkin’ Donuts private in 2005, said it respects the Hardee’s and Carl’s Jr. brands and wouldn’t shake up management.

Yet many predict THL will push for cost cuts and discounts to boost restaurant traffic and reverse recent sales declines.

That’s a strategy Puzder has shunned since he took over as CKE’s CEO in 2000. He turned around the Hardee’s brand and reenergized Carl’s Jr. with a revamped menu, renovated stores, and edgy advertising. He has consistently marketed the quality of CKE’s hamburgers rather than engage in price cutting with much larger national competitors such as McDonald’s and Burger King.

“Our competitors aren’t selling food. They are selling a price point,” Puzder said last year. “We’re selling food. If people are selling something for 99 cents, it’s either inedible or they are losing money.”

But as CKE confronts recent same-store sales declines, analyst Conrad Lyon of Global Hunter Securities said he wouldn’t be surprised if the company plays “with pricing a little more aggressively” and starts offering more discounts and “value offerings” to drive up traffic.

“Expect cost cuts, perhaps massive ones, especially cuts in labor,” wrote Dan Mitchell on the Daily Bread food-business blog on Slate’s The Big Money site. “And expect those cuts to be even deeper than they otherwise might have been, because Thomas Lee will almost certainly lower prices to increase foot traffic, and margins are already thin and getting thinner.”

Puzder declined to be interviewed for this story, citing sensitivity to Security and Exchange Commission filings still due in connection with the THL buyout.