It wants to be HOT HOT HOT!!!!! I wanna get very very very brown!!!!
I got this information from a greek website.......hope it helps........

"The first two weeks of August see daytime temperatures mid 30's to 40 - with high humidity. Evenings are warm and humid. Without air-conditioning it may be difficult to sleep. Glorious sunny days give way to packed beaches and even busier Tavernas. The sea is at bath temperature."

Hi Emma, the weather in Kefalonia can be a bit changeable in May. You are there towards the end of the rainy season so don't be surprised if you get a few days rain. One of my friends always visits the second and third weeks in May and one year he was out walking in T shirt and shorts when it clouded over. Within minutes huge hailstones came down! This lasted for about ten minutes.......... the ground was white! The sun soon came out, however and all was back to normal!
In general, it will be hot during the day but evenings can be a bit cool so take something warm for the evenings just in case. As the month wears on it does get warmer. The swimming pools may be a bit on the cold side though as they will have only recently been filled.
May is a great time to visit as the island is really fresh and green with lots of wild flowers..............Enjoy!