The first pic looks like pythium (root rot). The second pic looks healthy.
Water holds dissolved oxygen (this prevents pythium). Waters ability to hold dissolved oxygen is very limited at temperatures above 70 degrees F. Therefore keeping the water around 65 degrees will help the DO levels stay up. Water pumps and air pumps add heat. Your aquarium chiller may be required at a different location in your setup to get the water cool enough to hold oxygen. The best way to aerate water IME is the waterfall effect.
There are products out there that can help, beneficial bacteria, hydroguard and the like but water temperature is the main cause of pythium does not like oxygen and warm water won't hold enough dissolved oxygen.
"Pythium is a genus of parasitic oomycotes. They were formerly classified as fungi. Most species are plant parasites, but Pythium insidiosum is an important pathogen of animals, causing pythiosis. The feet of the fungus gnat are frequently a vector for their transmission."
I hope this information helps.
As in itself your remarks are true (that water can hold more DO in warmer temperatures, and plenty of DO can help prevent Pythium) you are drawing not the right conclusions.
At 20 C (68 Fahrenheit) water can hold about 9.1 mg per liter
At 26 C (79 Fahrenheit) water can hold about 8.1 mg per liter
So that is just a small difference.
And that is in still standing water. The moment you start moving this water, the DO level will stay at 8.1, even when the plants start absorbing the DO. So with the right aeration there is always more DO available then any root can absorb. In cold water or warmer water. (if your res or tote is big enough of course)
An infection by Pythium can be caused by several reasons.
Quality and resistance of the plants;
High temperature (> 30 ° C) or strong changes in root and / or substrate temperature;
Too much root pressure. A too high root pressure can lead to cell weakness and glassiness. This gives the pythium mold more chance to penetrate the root;
Wrong fertilization or high EC value, making roots more sensitive or less resistant;
Low oxygen content in the substrate. At low oxygen values the growth of the pythium increases strongly.
Damage to root or plant during crop treatment.
So you are right that the more DO your roots get, the more you help to prevent Pythium.
But it is also important to work clean, desinfect after grows, making sure that you add enough DO to whatever hydro-system you are using.
If you keep the watertemperature down but you don't add new DO, you are doing the wrong thing.
Just make sure that your DO levels are always at their maximum and keep the temperature in a certain range, then it is ok.