You might want to read these two links.
http://www.mayoclinic.com/health/exercise/HQ00316
http://www.weatherimages.org/data/heatindex.html
Together, they suggest one exercise extreme care when exercising in hot and humid enviornments. Greece is definitely that type of environment. Heavier people tend to not manage core body temps as effectively as leaner-bodied people. That's the issue.
FWIW, researching over-hydration suggests the number of over-hydration reports is miniscule in comparison to dehydration reports. I live in South Louisiana and don't even think about over-hydration in the summer --- I carry 3 water bottles and routinely empty them on rides, sometimes multiple times on the same ride. YMMV
Drinking 2-3 liters of water per day is not excessive for the average person, even when not exercising in the heat.