We just did the pirates league last week and I was not impressed with their costume selection at all. I bought a pirate costume for DS at Children's Place that was absolutely adorable and was MUCH MUCH nicer than the ones they sell there. Best part was it was only $15!!!!! The boy next to us had the same costume, LOL. It seriously is so perfect for this, I would encourage you to check Ebay before shelling out the major bucks for the inferior Disney ones.
We were there last May and while it was quite comfortable touring in shorts/tshirts, I think any child would be hot in a pirate costume after a little. That doesn't even factor in if there is a heat wave (pretty common for that time of year). I would only plan on a full costume for pictures and MAYBE the top could stay on for the better part of the day with shorts if it is seasonable and you mainly hit air conditioned attractions.
