From the discussions here, I took my darlingtonia out of the tray of water. I made an easy water-dripping "machine", see the following picture. It consists of a bottle of distilled water, a deep tray, and a stand. I made a small hole in the bottom of the bottle, such that the water is dripping into the darlingtonia pot. The pot does not stand in water, but on a stand in a deep tray. So the water continues go through the darlingtonia pot and is stored in the deep tray. Since the hole is very small, one gallon water can drip for more than 24 hours. When the deep tray is full of water, I pour the water into the water bottle, so that the dripping continues.
Note that the darlingtonia pot is covered with platiniridium, which cut from a tray for baking cake. The platiniridium "cloth" reflects most of sunlight, preventing the pot from heated by direct sunlight.
Here are two pictures of my three-year-old darlingtonia:
People that use circulating water methods generally report good results. I would use a higher tech solution and get a solar powered low volume fountain pump.
If you are near the coast in San Diego such methods are probably not needed but certainly do no harm.
Reading back issues of CPN there was mention that Leo Song and others determined that one of the keys to keeping this species alive is to keep the root temperatures from going over 21 degrees Centigrade.
This is easily achieved in the California coastal climates with oversized, thick walled pots.
Yes, it's growing well under the direct sunlight. It has developed 6+ new pitchers. But I think it thrives due to two reasons. One is the moving water. Another is the avoiding heating the pot. I used Aluminum Foil to warp the pot, preventing the direct sunlight heating the pot.
Here are the pics of the biggest pitcher taken in April :