Out of a moment of whimsy, I decided to build a heating system for a toilet seat.  A web search shows that these items are very popular in Japan, and Kohler has a commercially available unit for under $100.  However, its size was not right for our use.  As a result, I assembled a unit from scratch.

First, I acquired some foil heaters from the Minco corporation that were each about 20.1 ohms of resistance (part no:HK5427R20.1L12B).  The cost is unknown.  They are good to more than one Watt per square inch, so I had plenty of margin on that parameter.  I then purchased a new seat for about $15.  I selected a "molded wood" type opposed to a plastic one, as I suspect that its thermal conduction is better.  I also think it is easier to machine and cut.  Onto the sides I attached the two Minco Foil heaters, which I wired in series to a small electrical jack on the edge of the wood.  I embedded the wires in a groove that I made with a circular saw, and then filled the groove with epoxy to replace the structural strength of the material that I had removed.

After this was assembled, I then spray painted the whole face to restore the uniform appearance.  This resulted in a very clean look, with only a small silver jack visible from the side.  This jack accepts a plug for the electrical power.

I used an AC transformer rated at 16Vac.  With the 40 ohm load, this results in about 3.2 Watts per foil heater.  This very small amount of power heats the foil side to a noticeably warm temperature (about 90F), but is cooler and more evenly distributed on the top side of the seat.  I measured the total power draw with my "Kill-A-Watt" power-meter, and it was only 11 W (about 4 W lost in the transformer), or about one penny per day of cost to run this device.

View of the installed seat.  Note the GFCI protected outlet that I installed just next to the toilet.  After a few months use in the winter, I will decide on the right voltage, and will replace the large transformer and wires for a more clean look.
 

Long term update

• 9/8/2002.  Unit is assembled and installed.  Final selection of transformer will occur when the proper voltage has been decided.
• 12/21/2002.  After a few months of winter weather use it has become clear that the initial guess for the transformer voltage is exactly right (16Vac).
• 11/10/2019. I was able to measure the power draw of the original unit above (which continues to work well).  It draws 0.49 Amps at 18.72 Volts.  This is an actual resistance of 38 ohms and a total power of 9.17 Watts.  
• 11/23/2019.  Built a new unit for a second bathroom.  I designed the system to dissipate 10 Watts total based on the data from the original unit.  The heaters were from seller "crownones" on Ebay.  I used two that are 5 ohm each, so they were put in series.  I used a Dremel with a ball cutter to cut a groove for the wires, and then covered them with epoxy.

Links

• Minco Foil Heaters
• Commercially available heated seat from Kohler