Two of the NFL’s hottest teams are preparing to play here Sunday. Anyone who suggested a month ago that one of them would be the Cleveland Browns would have been laughed out of the room.

Even as the Washington Redskins were bottoming out at 3-6, the Browns were doing them better, dropping to 2-8 a week later. As Washington has fashioned its four-game winning streak, the Browns have been even more surprising, taking three straight for the first time since 2009. The Browns had given little indication that they were about to shed their well-earned reputation as one of the worst franchises in football.

The Browns’ surge brings with it implications that extend beyond their place in the standings. The ownership change from Randy Lerner to Jimmy Haslam had left the futures of General Manager Tom Heckert and Coach Pat Shurmur in question. The consensus of folks sitting down for Thanksgiving dinner was that not a tear would be shed if both were fired after the season.

Three victories have dramatically changed that perception. Persistent reports that new chief executive Joe Banner already has decided to replace Heckert with former Browns director of player personnel Michael Lombardi are eliciting outrage, and the once-embattled Shurmur is gaining support amid rumors that Banner is scouring the college ranks for a new coach.

Heckert arrived in 2010 facing the enormous task of transforming an old, slow roster that was short on talent into a younger, more athletic squad. The players Heckert has selected, including many in the lower rounds, have begun to blossom. His three drafts have netted 13 starters.

The Post Sports Live crew put themselves in Mike Shanahan’s shoes and debate whether the Redskins head coach should start a less-than-100% Robert Griffin III over backup quarterback Kirk Cousins this week in Cleveland. (The Washington Post)

His 2012 picks have proven particularly productive. Featured running back Trent Richardson and right tackle Mitchell Schwartz have shown Pro Bowl potential, and quarterback Brandon Weeden may have solved a problem that has dogged the franchise since Bernie Kosar was slinging passes around Cleveland Stadium more than two decades ago.

Some fans have yet to be persuaded that three wins against weak competition (Pittsburgh without Ben Roethlisberger, Oakland and Kansas City) negate the fact that Shurmur’s team had lost 19 of its previous 23 games. But the Browns are unquestionably performing with passion for their coach. They have played every opponent except the New York Giants down to the wire.

Their inability to finish could be attributed to youth and inexperience, and they may have learned how to win in the last three weeks with a perseverance that is a reflection on Shurmur. They might even be in the hunt for the playoffs, some argue, if not for a four-game drug suspension served by top cornerback Joe Haden (Friendly High). The Browns lost all four games as opponents picked on their severely weakened secondary.

Most encouraging has been the play of two wide receivers, Greg Little and rookie Josh Gordon, who are showing signs of turning a long-term weakness into a strength. Gordon, taken in the supplemental draft for a second-round pick, has displayed greater potential than any Browns receiver since the late 1980s. He has been particularly explosive in this three-game run, snagging 18 passes for 262 yards.

“He’s starting to get a feel for what he can do,” Weeden said last week. “The sky is the limit for that guy. He’s talented, he’s tall, he’s long, he’s fast. He can catch the ball well. He does all the things you would want. I’m glad he’s on our side.”

But it’s the Browns’ defense, which lacks premier talent outside of Haden, that has keyed the team’s three-game winning streak. The Browns have yielded an average of just 12.8 points and four total touchdowns during the mini-tear. Their hard-hitting pass rush has emerged as one of the most effective in the NFL. Defensive ends Frostee Rucker and Juqua Parker, the only major free agent acquisitions made by Heckert during the offseason, have combined for nine sacks.

Uncertainty over the status of Redskins quarterback Robert Griffin III could make the defense’s preparation more difficult, especially considering the difference in style between Griffin and his backup, fellow rookie Kirk Cousins.

“I’m sure we’re going to hear a lot of different things this week,” Shurmur said. “We have to prepare for the Redskins’ offense. We can’t get caught up preparing for just one player.”

Shurmur said that using Browns backup quarterback Colt McCoy to play the role of Griffin in practice is far from ideal, but simulating the Redskins’ star with the talent on hand is impossible.

“I’m not sure we have anyone who can simulate his speed,” Shurmur conceded.

The Browns also don’t have many defenders to match Griffin’s speed. That’s why they are better off if the Redskins’ medical staff chooses to give the NFL’s top-rated quarterback another week to recover.