Beasely is an interesting mess. There's been something wrong wiht him mentally since as long as he has been in the publci eye. People always make excuses for guys like like, Artest, whatever. But you know. Or should. They just do not act/respond like normal people. To top it off, he is incredibly undersized -- he can't be a full time PF for anybody but D'Antoni.
And yet, and here is the interesting part, he put up EXTREMELY impresive numbers in limited minutes last year. 13.9pts 5.4 rebs in 24.8min? That's basically 26pts 10rebs/per 48. And it was viewed as disappointing.
As for what Miami would want, consider this:
1) Miami has done an AMAZING job clearing megacaproom for this upcoming summer and the LeBron sweepstakes. The onyl players on the entire roster who are not enders are their kids (Beasely, Chalmers, Diawara). Do they want even more room? Room to compeltely start over? Don't know, but a team like that with such a clear strategy might really love KTs ending contract, and he even plays the same position.
2) Miami is also, of course, desperately trying to impress Dwayne Wade so he'll stay with them. We can't help much directly, but if the Heat were satisfied with their cap room what about a three way deal? Go to Philly, offer them Beno & Noc (since they no longer have a starting PG with Miller gone), have them move Brand to Miami, take back Jrue Holiday, Beasely, and contracts. Philly fortifies their playoff position again, Miami gets a veteran former All Stare frontcourt of Jermaine/Brand, and we come out smelling like roses with the kids (maybe smelling too good -- when you smell that good somebody else probably is not interested).