I leave my t-shirts, towels, water bottle, and such at my chair in a tote bag. I leave wallets, dry clothes to wear after the day, shoes, and money in a locker. I don't know what the lockers are like in the rest of Disney (we haven't used one in years) but at the water parks you can use it all day for one price.
On the water temps, BB is kept cooler to go along with its theming, while TL was fairly warm all over when we were there last.