The weather early July is warm (20-30 degrees C) and dry; rain is rare. You don't need a jacket during the day, typically not even at night. It is not unpleasantly hot but the sun is powerful, so one does not sit in the sun, esp. on mid-day, and one needs to drink a fair amount of water. The Anatolia/ACT buildings have air-conditioning.
Details on the climate for Thessaloniki:
(compare this to a place you know, for perspective http://weatherspark.com)