©2013 Green Building Advisor. From The Taunton Press, Inc., publisher of Fine Homebuilding Magazine.
First off, my wife just joked that I used a photo of a “male bathroom”: seat up and two rolls of toilet paper.
Regarding the heat savings mentioned in the headline, we'll see... I haven't done the math yet. But it is a minor claim occasionally made alongside the claim that these toilets save water.
Some manufacturers of dual-flush or low-flow toilets make extravagant claims on water savings; and tacked onto the end of the marketing copy there is sometimes a blurb on heat savings:
Wait... what? One of these things is not like the other. If this is true, how does reducing your toilet water use affect heat loss?
First off, admit it... you didn't think that a toilet would have anything to do with energy efficiency. Saving water, sure — just not energy savings. But the heating dynamics of a house are ridiculously complicated and interconnected.
One of those dynamics is internal net heat gainIncrease in the amount of heat in a space, including heat transferred from outside (in the form of solar radiation) and heat generated within by people, lights, mechanical systems, and other sources. See heat loss.. Anything that radiates heat within the enclosure will add BTUs  to the building. Remember your last indoor concert (Dropkick Murphy's, St. Patrick's Day 2011... I should get out more)? Remember how sweltering hot it was? That's because all those hundreds of bodies are adding heat into the building enclosure.
In the home, every incandescent light bulb , television, pet, and person adds BTUs to the house's internal heat load. Conversely, there are some items which absorb heat and cool the house. Cold water pipes are one; and another is the water sitting in your toilet tank.
Every time someone flushes the toilet, the water in the toilet tank is replaced with ground water. In Maine (and most northern climates), the ground water is colder than room temperature. The cold toilet tank will absorb heat until it reaches room temperature.
Fortunately, the math is super-straightforward.
According to the EPA, toilets account for 110 gallons of water use per day on average. Three quarters of this is for liquid waste and one quarter is... not. (Distasteful, I know, but difficult to avoid mentioning).
I'll be using info about my house, since... why not? Our dual-flush toilet uses 3.5 gallons for a full flush and 1.5 gallon for a partial flush. We live in Portland, Maine, and our handy USGS groundwater map shows that the ground water temperature ranges from around 48°F to 50°F.
So let's review all the data:
Important Note: Let's not quibble about the numbers. These numbers could be wildly off from real-world heat loss measurements, but we're painting in broad strokes here. The idea is to illustrate some thermodynamic calculations, not to use experimental precision and accuracy.
Just pause for a moment and think about that: nearly 400 pounds of water. OK, time's up.
A BTU is the amount of heat needed to raise the temperature of 1 pound of water by 1 F°. (See this article  in which I talk about BTUs in a bit more detail.)
Knowing that there are approximately 138,000 BTU in a gallon of #2 heating oil, we get 0.055 gallons of oil per day, or a bit over 20 gallons of oil per year.
Holy crap! That's nearly $80 a year just heating your cold, cold toilet water. That's ridiculous. We should mandate a Federal "swappin' out your inefficient toilet" Task Force, right?
Well... hold your toilet-fixing horses, mister. There are many, many caveats here.
First, will you use the partial-flush feature of your new toilet? Ceiling fans, programmable thermostats, zoned heating systems... there's a long list of mechanical systems in your house which could (emphasis on could) save you money but largely don't. And the why in this equation rests squarely on the fact that people don't use them properly. In our house, we make a conscientious effort to use our dual-flush system, but the results depend on use.
Second, I pulled a wee sleight-of-hand in using my house. There are only a small handful of states as cold as Maine, and only one (Alaska) that is significantly colder. Most states have warmer climates and warmer groundwater. Instead of warming from 50°F to 70°F, it may be 62°F to 70°F, with a corresponding reduction in heat loss.
Third, dual-flush systems are much more mechanically complex than classic plunger systems. So they're more apt to have issues than a simpler set-up. There's not much savings of any kind if a gasket continually leaks water.
Fourth is the question of overall water use. Households with only one or two members won't use anywhere near as many gallons for toilet flushing as are shown in the calculations above. Conversely, a very large family is apt to slack off or have some members who ignore the dual-flush feature. They've forgotten the first rule of the Dual-Flush Club: Don't forget to use the dual flush.
Fifth, fossil fuels won't be needed to produce space heat for 365 days a year. The toilet tank may be warming up to room temperature, but for big chunks of the year it will be heated by the warm summer sun, not by your oil boiler.
Last, my math makes one rather silly assumption: that trips to the bathroom will be sufficiently spaced out to allow the cold water to fully reach room temperature. Not bloody likely.
So is there any benefit? The minor point is that, yes, in our neck of the woods there is some small heat savings benefit to dual-flush toilets or toilets with reduced flush volumes.
The broader point is that everything that is hot or cold is a component of your home's internal heat load. Once you start thinking about your house this way, the cooling benefit of a heavy window shade on a sunny day is more obvious, and uninsulated cold water pipes are not quite as innocuous. They're all part of how well your house's enclosure controls temperature.