Yeah, there's quite a difference in warm weather comfort between plastic backed and cloth backed. I'm not sure if you need to wear them, or just wear for fun, but when it's warmer, you'll probably find more comfort in something that is thinner and cloth backed. Pull-on types have seemed to be to be rather comfortable in summer, though they certainly don't absorb quite as much as traditional tape on's.
If you're looking for something that would be bought at the store, my best bet for you would be maybe the CVS brand briefs, as they are cloth backed and I think they are almost identical to the walgreens brand and prevail. All three are very similar that I think they actually may be the same diaper, just a different package. They are on par with Depend briefs, though they are less expensive generally. Other than that, some places, mainly independent pharmacies and medical supply stores will carry attends. These certainly aren't as good as attends used to be, but are I think a step better than generic store brands. If you are going the attends route, get the breathable briefs, and absorbency is rated by numbers, the higher the number, the more absorbent. I've tried the #7, but I think they make the breathable in 8 and 9 as well, with those being a little more absorbent.
If you are ordering online, most of the great diapers are plastic backed, but you might find the Abena Air Plus, I think they are called and I think someone else mentioned them. I haven't tried them, but they are supposed to be a bit more breathable. Also, Abena makes a wierd diaper, I think it's called the abri-wing, these are pretty good for warm weather too, as they have the benefit of leaving a bit more of your hips exposed for better breathability, and the waistband is not plastic, but rather that type of "cloth" that they use on disposable diapers.