First of all, the Heat were straight up making shots, especially from outside. Cook hit three in a row early that sort of set the tone for them, as they went on to set a franchise playoff record for threes made. I think they had 15, and they made those at over a 50% clip. O'Neal was MUCH better, and gave the Hawks problems wwhen they tried to double on Wade. They stopped doubling Wade for a while, and he made them pay at the end of the first half. He scored 13 in a row for the Heat to close that half.
Defensively, the Heat were MUCH better. Only one or two transition buckets. Joe Johnson was in foul trouble all night and wasn't a factor (refs got the whistles back out for this one on both ends, unlike the first game). Bibby was the only saving grace for the Hawks, as he hit about 5 threes in the game too. Heat had a comfortable 15 pointish lead for mush of the game. Hawks cut it to 5 with 5 minutes to play, but that was as close as they got. They pretty much seemed content to trade buckets with the Heat, hoping that they would miss, but they didn't.
Personally I think that the Hawks came out expecting to win easily after the results of game 1. I hope the message got sent tot them, but thats neither here nor there... Hope this helped. If you have any other questions, let me know.
Oh, and Beasley was better than game 1, but still seemed very shaky with the jumper. He was more aggressive in getting to the rim though, and thats where he got the majority of his points.