Ok, since you didn't mention the exact time of June, I have written, my personal experience of what to expect at
Disneyland, which truly seems to have it's own weather patterns, generally if you look at Anaheim in June and add about 5 degrees you are about right for Disneyland, I have no idea why that is. This is coming from a local that goes at all times of the year, here is approximately what to expect during the different times of the month. And as always your mileage may vary, also always bring a change of close, if you dress for warmer weather bring a change of clothes for colder weather and vice versa, it always seems to be the opposite of how you are dressed. Also always bring a light jacket for night if you tend to get cold.
June 1-10: Mornings: About 60-70 Degrees
Afternoons: About 70-78 Degrees
Evenings: About 60-70 Degrees
Nights: About 50-60 Degrees
June 11-20: Mornings: About 65-75 Degrees
Afternoons: About 75-83 Degrees
Evenings: About 68-73 Degrees
Nights: About 60-65 Degrees:
June 21-30: Mornings: About 70-75 Degrees
Afternoons: About 80-110 Degrees
Evenings: About 70-90 Degrees
Nights: About 70-75 Degrees