Greece in August will indeed be very hot. Are you the people going to Kos?
each person needs: a week of underwear, three sets of swimwear (one on, one to change into, one rinsed in the shower the previous night and drying on the balcony), a few t-shirts, light long trousers and one light long-sleeved top (evening cover up against mosquitoes). Swimwear for kids is sunsuits to protect against UV. Sunhats all round. Perhaps an extra long sleeved loose top or two. Flip flops, beach shoes, one pair trainers to wear on journey/for any sightseeing. Maybe one fleece top each for the plane/transfer coach (can be over airconditioned).
if staying more than a week, pack a bit more or do a bit of laundry.
whatever you need in the way of kids/baby stuff. Toiletries. Medication (of course Greece has pharmacies but you don't want to be finding one when you are ill). NB nothing with codeine in, illegal in Greece.
lots of suncream, some insect repellent, sunglasses. Books/kindles. A euro adapter or two.
do not take hairdryer (it's hot in Greece, just sit outside for 10 mins) straighteners (far too hot to use), too much makeup (it slides off), perfume (bad in the sun, attracts mosquitoes in the evening), jeans (too hot), high heels (silly on cobbles/marble).
that's it!