How do I control the temperature of water for an extended period of time?
You can try to set up my at-home on-the-cheap monkey-at-the-controls sous-vide machine.  I take a nearly full 22 quart stock pot with an analog instant read thermometer to monitor the temperature and watch the temperature and adjust the dial accordingly.

With this only needing 30 minutes you probably just want to get the water to exactly 72 degrees C and then immerse the potatoes without adding any heat.  The amount of energy in 20 quarts of water is phenomenal and you won't lose a lot of heat to the air.

Alternatively you could get 72 degree water and a beer cooler and try that way for the extra insulation.