How are public spaces in greece? Any large "free" sources of AC? Homeless in the US sometimes use this method to avoid severe heat exposure, hanging out in say a mall, public library, airport bag claim, staying underground in the subway system, or riding an air conditioned bus around.

If I had to make an educated guess, I'd say Greece doesn't think about these types of public spaces as much as other countries do and the ones that do exist are probably a bit hostile towards the homeless.