Another stat you should remember regarding organic farming, and apropos of heatwaves and drought: According to Rodale Institute's long-running side-by-side trials of organic and non-organic farming, in conditions of drought organic corn yields were 31% higher than non-organic.
As for why, over at Mother Jones, Tom Philpott gives thorough detail on the subject, but the quick version is this: It comes down to the differences in soil managed through chemical fertilizers versus those managed organically.
If you're an organic farmer, you don't have the luxury of blasting your soil with straight nitrogen. To replenish nutrients, you have to have physical stuff that contains nitrogen bound up in organic matter—think compost and manure. You can also grow legume cover crops that trap nitrogen from the air and deliver it to the roots of plants in a form that can be taken into the soil. In this case, too, you're adding a nice dose of organic matter along with nitrogen, in the form of the plants that rot in the ground when the cover crops does. And, like conventional farmers, you get the benefit of crop residues left in the field. As a result of these difference, organically managed soils trap more carbon in the soil—and all of that carbon allows these soils to hold in water and nutrients better.