Magic Kingdom has a good spread of spots to get ice water throughout the park. The general rule of thumb at Walt Disney World is anywhere that sells fountain sodas you can also get cups of ice water from. Ice water usually comes in kid size cups so make sure to ask for 2-3 cups per person to refill your reusable waterbottle. 

As you make your way through your day hitting the top attractions, make sure to take some breaks in the various shows & spots to get some air conditioning. A few tips I have on these are: 

• Tiki Room - Grab a Dole Whip next door and eat it in the show to cool down. 

• Hall of Presidents - Top tier nap spot and duration!

• Dumbo ride queue play area - Absolute must with kids!

As for dining you have a few options for quick sevice locations inside. My favorites are Cosmic Rays for their standard theme-park burgers & chicken options and Columbia Harbor House. If you opt for Columbia Harbor House make sure to check to see if the upstairs is open! It's never busy up there and is a great spot for a break (and to people watch from the windows!). 

Here at EPCOT my #1 tip is sunscreen. My #2 tip is an umbrella, especially if it's bright and sunny with no chance of rain! When you are half way around World Showcase in 105 degree weather with the sun beating down on you, you will truly wish you had an umbrella for shade. 

Luckily, there is a semi-decent number of spots spaced around the park where you can refill your water supply without paying the $3.75 for a bottle of water. Shade and AC on the otherhand is hard to come by once you are in World Showcase. That's why I recommend spending the hottest part of the day in the front of the park where you have lots of opportunities for both rides and AC cool-off spots. Once the heat of the day has passed then make your way around World Showcase. *note - this works best if you want to enjoy the festivals but you will need to tough out the heat 'around the world' if you want to see most entertainment in the various countries or meet Characters. 

For dining you should really take advantage of the festival food booths or any of the great sit-down meals at EPCOT but if you need a break there are some quick service spots that will work good too. 

Hollywood Studios is comparatively a small theme park when you're used to walking around EPCOT in the heat. You have plenty of opportunities to take a break indoors and get something to drink. 

My favorite place to refill my water at Hollywood Studios is Backlot Express because it is a self-serve fountain soda machine meaning you don't have to ask for 2-3 cups of water to fill up your own water bottle. 

Nearby is my favorite place to eat a quick lunch and cool down - PizzeRizzo. The upstairs of this pizza quick-service location has a little dance floor where kids can dance around while you decompress and it's never busy up there. 

Here at the most humid park at Walt Disney World, Animal Kingdom has a decent amount of shade in most of the park but the stiffling heat will still make you search out those sweet water spots. My favorites are #1 and #2 on this map because they are self-serve fountain soda machines. 

There are really no good spots to sit inside and cool down besides scheduled shows and dining locations at Animal Kingdom. Don't skip out on the Festival of the Lion King show - This 30-40 min show in dimly lit stadium seating is a good break from the heat. If you want a place indoors to sit and decompress without watching a show, Restaurantosaurus is your spot to be. The other two spots on the dining list may restrict entry to diners only (Satu'li), or have shortened hours (Pizzafari). 

If all else fails, head over to Kali River Rapids! The water ride will cool you right down and there's a little fountain by the bathrooms/lockers there that kids like to splash in to cool down too.