Hi Pimo,
We've been going to Greece in August ever since our (now teenage) daughter started school, so a similar age. We've never had a problem, and now she thinks it isn't really a Greek holiday if the thermometer is under 30 C.
Our tips have always been - go to the beach early or late, drink plenty of water and if your child does get dehydrated, we have always found fresh watermelon juice (or watermelon) is a marvellous rehydrant. Works for adults too.
We had a crescent shaped beach tent which would get very hot, because it has to be set up with the back to the wind to stop it blowing away. We then found one with four open sides, and attached a sarong to the sunny side with bulldog clips and tent pegs. The only problem is putting it up and taking it down in the wind.
I haven't been to Plakias in June, but I understand that the very strong winds don't pick up until July. August is always very windy, leading to sand-blasting on some beaches.
I am looking forward to the time when we are no longer limited to school holidays and June or September would certainly be my preference, but August is fine. Greece in August or not at all? - the choice seems clear!
Arnaki