I started about a month ago. I would feel dead tired after the warmups, and I'd be panting like a dog after a few minutes of rolling.
Yesterday I did about 25 minutes of rolling with some resistance drilling before hand, and was fine at the end of class. When I play my guard in particular, I don't breathe heavy at all.
Part of it is being in better condition, but more importantly it's learning how to relax while rolling.
I weigh 212 pounds, and could stand to lose another 20 pounds. Not a small guy, and not in amazing shape.
I still work up a good sweat though. My gi is soaked by the the time class is over, and I'm definitely tired. It's just that I don't blow everything I have all at once.