I read some misinformation here. Where does the 70 degree temp come from? I understand D.O., but don't understand how taking a fish from 85 degree water and putting the fish in 70 degree water isn't going to put the fish in shock. As far as adding ice..... by using an automatic ice maker to get your ice doesn't mean it's pure. Yes, there is a filter inline to the water supply, but this is normally just a screen. Newer refridgerator icemakers may, or may not have purifying filters. The problem with adding ice is that the chlorine burns the fishes gills and they can no longer absorb oxygen. An amount of chlorinated water below 20% of the livewell volume probably wont be enough to harm the fish. I don't think your carry enough ice to reach that amount.
As far as not recirculating warm water, this is just wrong. The purpose of recirculating is to infuse oxygen into the water. Aerators also do this. By continually recirculating your livewell + adding fresh water through the aeration pump and system periodicly you shouldn't lose fish.