I wonder if it is possible

[Alpo]

To have a thermostat on a water heater so precise that it would keep water to the 10th of a degree?

 

There's an old movie called HOW TO MURDER YOUR WIFE. It starts off with Charles ("I am Mr Ford's man") giving you a guided tour of the premises.

 

"This is Mr Ford's townhouse."

 

"This is Mr Ford's rooftop garden."

 

"This is Mr Ford's shower, set to precisely ninety-eight point SEVEN degrees - Mr Ford's body temperature."

 

I thought that was a very cool bit of business. I don't think they had the ability to do that back in the 60s when the movie was made, but I wonder if they could do it today?

[Marshal Mo Hare, SASS #45984]

Given enough money…. It can be done.  I would engineer it, for my usual fee, of course.

[Dusty Devil Dale]

Every thermostat has a  factory set hysteresis, which is a particular number of degrees above or below the setting at which the burner or element turns on or turns off.  

 

I suppose it would be possible to set the hysteresis  very tightly around the nominal setting, but the heating element or burner would be turning on and off so rapidly that a very large fraction of the energy would be wasted. 

 

 Usually hysteresis is about 3 deg F plus for shut off and about 1 degree F minus for turn on.  So set at 68 deg, it turns on at 67 and off at about 71 for a four deg range of variation. 

 

[Cholla]

We used to install these if absolute control was required but I only used them for air, not water.

https://necc-controls.com/thermostats/accustat/

 

A proportional control would be better but it requires more equipment and more cost. I also think most folks would find 98.7 too cold for a bath or shower.