Things often said about olive oil—that most of it is fake, that it's a good source of Omega-3, that 'first cold pressing' means anything— are dirty oily lies. tl;dr: buy only fresh, expensive, brand-name extra-virgin oil in tins, or just get something cheap and healthy that isn't olive oil.
Here the author addresses claims that transfats lurk at even medium heat:
6. Go ahead and turn up the heat. Because of its high polyphenolic content, extra-virgin is more stable than many other oils. The widely held belief that disaster lurks at temperatures above 250 degrees Fahrenheit is simply wrong. Extra-virgin remains stable up to about 410 degrees or a bit higher, depending on the extent of filtration (less filtered means lower temperatures). So deep-frying—best at 350 to 360 degrees—is more than acceptable. Use olive oil in baking too: Cakes gain a moist, rich texture when it’s swapped in for butter, as in the recipe for gluten-free blueberry muffins above.