it actually is a death sentence, literally a matter of time before that water smells like a blueboy and your tossin that plant
I have a friend that does DWC on a small scale, 1-2 plants at a time and he doesn't cool his res at all. His grow sits in his 90-95 degree garage. He has never had a problem with root rot or algae. He simply ups the peroxide once a week or so and makes sure the root zone is getting tons of fresh air. As for putting the air pump below the water level, it can be done you just have to get one of those backflow preventers to go between the pump and the res. Here one of these badboys http://www.petsmart.com/product/index.jsp?productId=2752253&lmdn=Fish