We haven't been in the last week of June, but we go during the first 2 weeks of June. What I can tell you is that it is HOT. Be prepared to take lots of breaks and drink lots of water. Also, plan in plenty of shows that are inside during the middle of the day so you can get some air conditioning and cool off some. Also, the crowds will be pretty intense so go to each park with a basic plan of what you want to ride and see and about when you want to do so that you can take full advantage of Fast Pass, but be flexible enough to change when you see a short line or have to deal with a break down.