Ahh we just did the kindergarten zoo trip:) Surprisingly it was the coldest day EVER - Texas - go figure.
I don't typically freeze unless I know it is going to be Hotter than hades.
As a volunteer, they split the kids up in groups of three of four and give the lunches to the chaperones in the drawstring backpacks of three or four lunches. No coolers. Check with your teacher, too.
Anyways. Target bags are good - ziplock bags. I have done ziplock bag of ICE inside the brown bag to keep things cool. The items really don't sweat so much that it tears the lunch sacks since they are really only in there for a few hours.
Also, for future reference the zoo is ok with insulated bags, it is the school that doesn't want (nor should they) keep up with a lunch box all day:)