I had the same problem last year but Amanda made the cutest hats this
way for St. Pat's Day and this
way for Easter. We determined that it could be the type of cups and the heat of the oven.
Practice with the temp of the oven using just one or two cups at a time. You have to keep a close eye on them because once they start melting, you have just seconds to let them melt before they are ruined.
Hopefully Amanda will see this and she might have some tips to add, too.
Good Luck with it! Posts some pics if they turn out right!!