High water temps lead to root rot and other diseases.
CAN lead to root rot and other diseases. Several members here have proven that the myth of running water temps at 68F - 72F are just that, myths. Depending on the chosen IPM methods used, temps as high as 78F are fine, but your IPM has to be on point. DO doesn't play as significant of a role at the scale most home growers operate at, so the argument of less DO being available is frankly BS.
Air pumps raising water temps is also negligible. I would be more concerned about the havoc they wreak on pH rather than the one or two degree increase they introduce to water temp. Granted in DWC your options for keeping the solution moving are limited, and again, this would be one of the last things I would concern myself with.
TL;DR: if you're running live, make sure you have adequate colonies of good bacteria. If you're running sterile, make sure you're consistently on top of it. Use enzymes in either case if you're not using pool shock. Forget about "ideal" temps of the solution, plants grow faster and healthier when their roots aren't cold (within reason). If res temps are over 80F, then you need to insulate better.