If you're carrying it in a bag and going in and out of attractions/AC you shouldn't have any problem. If you leave it in a car or have it in a sweaty pocket, yes, it will if hot enough. I've had enough chapstick containers melt into blobs in my car to always keep them in a small ziploc bag now but I never had trouble with one in my small park bag, even if sitting outside for a couple hours waiting for the parade, etc.