Are you wearing short sleeves? I found that wearing short sleeves seems to help the sweating, although there's still some that just comes from the body heat to body heat buildup. Also, opening the flap (well, I have a SPOC wrap, so it's not the same as a moby exactly) and fanning in a little air now and then.
Mei Tai is supposed to be for when they can hold their head up well on their own. Make sure if you use one, you tie it in the center, not under the bottom, to keep baby from slipping out. I found that Naomi just didn't sit in the mei tai well and sweated just as bad, though.
Oh, I do the cradle hold, just up on my breasts, btw--I'm a 38... uh, I? I don't think I'm still an H, but not sure how much my breasts have grown >_<
Talkative, AP SAHMama to my bright and spirited girls Lilly 10-15-06, Naomi 1-1-09 and Katarina 11-16-11 Musing Mommy