Welcome to the Disney Parks Moms Panel, Cindy. I'm so glad to hEAR you'll be heading to the Disneyland Resort at the beginning of summer.
Anaheim weather in late May and early June is typically mild. According to Accuweather's website, historically during that time of the year, Anaheim had temperatures in the upper 70s to lower 80s. It is usually sunny so be sure to apply sunscreen. Temperatures tend to dip after the sun goes down, so I usually pack along light jackets to wear at night as it can get chilly.
When we visited in February, it was unusually warm with temperatures in the mid to upper 80s. The pools were definitely being used then. Bring along your swim suits and goggles so you can take a dip in the pools during the warm afternoons. Splash Mountain and Grizzly River Run are also fun ways to cool off while you're in the parks.
I hope this information is helpful as you plan your upcoming trip to the Happiest Place on Earth, Cindy. Please visit me on the Panel again if you have further questions.
Have a magical day,
Kiki