Thanks TML for the reference to the problem with cooking with olive oil at high temperature.
We do this all the time at home on the basis that extra virgin olive oil is the healthiest, but googling around after reading your comment it is clear that you are right and the low smoke point of olive oil, especially extra virgin, makes it a bad choice for anything fried or my son's 'patent' oven potato wedgies.
Seems like organic rapeseed (canola) or sunflower is better for this purpose.
That's where my post was going to end, then I found a contrary view (as one always does on the internet!) -
here. They say that extra virgin olive oil (smoke point 208C) is fine for cooking and that '(extra) light olive oil' has one of the highest smoke points of any oil at 242C (though refined avocado oil at 271C is higher still). Figures agree with the much more extensive table
here (though here the temps are all in old-fashioned Farenheit).
Back to Google again. Olive oil brand
Filippo Berio state on their website: '(Our) Mild & Light (olive oil) has a high smoke point (200 – 210 degrees C)'. This I do think is probably reliable since I can't see why the maker would understate the smoke point, yet it is 32-42C below the figure above.

So... I'm thinking avocado oil is the safest choice when it is hard to be sure what temperature the oil is reaching (especially with frying). And keep the extra virgin olive oil for uncooked or low heat situations or as TML suggests for adding at the end of cooking.
When you mentioned 'mediterranean diet' TML were your referring to a specific diet or just the way that people in the Mediterranean eat (or should eat, or did eat in the good old days)?