After Zach Miller, who do Bears have at tight end?

A few hot days this August might lead to more eye rolls, sighs and non-answers from New England Patriots coach Bill Belichick than usual.

The Bears’ two joint practices with the Patriots and a preseason game in Foxborough, Massachusetts will give former Bears tight end Martellus Bennett many intimate opportunities to lash out at the team that considered him a problem and traded him away for a draft pick.

Another body slam of cornerback Kyle Fuller? More trash talk and shoving with outside linebacker Lamarr Houston after the whistle?

Or will Bennett just anger his teammates with slow strolls back to the huddle after catches?

Would anyone really be surprised if the mercurial Bennett breaks from the Patriots’ no-nonsense culture for a day or two?

For the Bears, facing Bennett that week is compelling because their current tight ends are less proven, talented and athletic than he is. That group will be counted on to vastly improve by the time the Bears head to New England, starting with organized team activities this week.

General manager Ryan Pace has done a commendable job improving many positions this offseason through free agency and the draft. But a slim draft class and an unappealing group of free agents deterred Pace’s efforts to strengthen tight end.

For now, tight end seemingly starts and ends with veteran Zach Miller, who signed a two-year deal, but still figures to face questions about his durability.

Beyond Miller, whose 15 games last season were his most since 2011, there are tight ends the Bears like and believe in, but each has to prove himself in some manner.

“We’re pushing them all together to work toward being the complete skill set,” tight ends coach Frank Smith said during rookie minicamp. “That’s ultimately what you’re looking for in the position group.”

Under Smith’s tutelage, Miller excelled last season with 34 catches for 439 yards and five touchdowns. But he also became a respectable blocker on the line and a useful fullback.

Now Smith is helping Rob Housler, who has 109 catches over five seasons with three teams, become a better blocker, and Khari Lee, who had one catch in his first, to be a better receiver.

Four-year veteran Greg Scruggs, who is listed at 6-3 and 310 pounds, will try to successfully switch to tight end after playing defensive line for years. And Gannon Sinclair (an undrafted waiver-wire pickup last year) and Ben Braunecker and Joe Sommers (two undrafted free-agent signings this year) will see what they can do at the NFL level after playing college ball at Missouri State, Harvard and Wisconsin-Oshkosh, respectively.

Housler and Lee will get the first opportunities after Miller during the offseason program, but the summer is the perfect time for younger players to push them.

That starts with Braunecker, an All-Ivy League selection at Harvard and one of the top all-around performers among tight ends at the NFL Scouting Combine. His skill set made him a highly desired free agent after the draft.

“He has good receiving skills and he had high production in college,” Smith said. “They used him in multiple spots so you saw that he was an intelligent player. He was able to do multiple things. He’s a tough guy.

“We’re just excited to see what he can do here and use those same qualities to provide positional flexibility with what he can do within the offense.”

Regardless of Braunecker’s potential, Bennett’s departure leaves more questions than answers on the field. But those are questions the Bears like having at the moment because they’re opportunities for players they want.

“A nice, strong, reliable, wide tight end is what the Bears are looking for right now,” Braunecker said. “It’s all about transitioning my physicality my footwork, my technique, stepping that up to the next level.”