T.S.
W.,
My children never had the oportunity for their lunches to be microwaved or refrigerated...whether in preschool or in elementary or middle school. An insulated lunch box works best. I always go for ones with removable plastic inserts, as they are easier to clean (but much more difficult to come by).
I use a small lunchbox ice, which can cost about a dollar. They last a long time.
As for foods, I make all kinds of sandwiches...or wraps. I also give yogurt. Both my kids love salads, so sometimes I do a nice sized salad with tuna or chicken or cheese on it for some protein. I also have given small containers with hummus, with some pita for dipping. My kids help me with their "menus." We ask them on the weekend what they might like for lunch that week. We actually do not do pb&j that often. My daughter also likes cold pasta for lunch...my son would not even want to touch it (me neither)! Maybe including your daughter in the process will help you come up with other ideas!
Good luck!