How do I control the temperature of water for an extended period of time? When making the "perfect" mash, Heston Blumenthal recommends cooking waxy spuds in hot water for half an hour at the temperature of 72 degrees Celsius, exactly. At 75 degrees stuff starts breaking down. 

I would like to try this out but am unsure how I can keep the temperature constant.  

What kitchen tools and process can I follow to measure the temperature throughout the process? Are there any tricks?
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.