I hope Bynum doesn't go to the Heat. If they're going after him, it's simply to keep other teams from acquiring him. I don't believe they actually want to utilize his abilities beyond being another body to keep Hibbert in check. The Heat are a guard-oriented team centered around Wade-Lebron and Bosh as the 3rd guy. Not exactly big-man friendly.
As hinted by Doc Rivers, the Clippers are probably not going to be looking into getting big man help until CP3 is back. They're not contending if he's not 100%.
The Hawks are an interesting team. They have some nice outside shooters like Korver to keep defenses honest for a big man inside. But I'm not sure if they're contenders even if they acquire Bynum. They can also offer him a little more than vet min.
One team nobody is talking about as far as contenders go is Portland. Lopez is a nice hustle big, but he stinks at guarding post players 1 vs 1. On top of that. Portland is basically a jump shooting team. They really don't have an interior presence offensively. However, their roster is full at 15 players. They'll need to waive a player or trade one away to acquire Bynum. Lopez' brother is currently injured. Portland could send Robin to Brooklyn to fill in for him. It's hard to find starting caliber centers who won't be upset if Brook comes back and puts them on the bench. Robin might fill that need for them.
Another team to look out for is Phoenix. They're way under the cap, so they can offer Bynum more than vet min. They have plenty of 3pt shooters, so he should have space to work in. Bynum gives them an interior presence that they don't have with Plumlee. The Phoenix medical staff is the best in the NBA, and has worked miracles for Shaq, Jermaine O'Neal and others who went there. If they can help Bynum, maybe he'll even return to all-star form.
"Every time he’s hurt, he always plays, he always comes through."
- Metta World Peace on teammate Kobe Bryant