To some extent drying clothes is generating heat (evaporation heat). If you're clever about it you might be able to avoid heating the (wet) clothes and rest of the contents of the dryer (or the outside!) too much. However evaporating water requires an incredible amount of energy, even if you just boil water away then most of the energy is still spent evaporating the water rather than heating the water, so it's not really too clear-cut that running a dryer hot is massively inefficient.
Edit: Also it's not that using lower-temperature water to convey heat is somehow more efficient, the thing with heat pumps is that they are more efficient at heating things to a lower temperature. If you're burning gas it doesn't really matter either way, you just get the energy out you put in.
> so it's not really too clear-cut that running a dryer hot is massively inefficient.
My heat pump dryer came with an energy estimate for various functions and loads. The various functions which shorten the time, or the functions which increase the heat (often related) are specified to use way more energy. To me, it's pretty clear, plus the manufacturer specifies it.
> Also it's not that using lower-temperature water to convey heat is somehow more efficient. [..] If you're burning gas it doesn't really matter either way, you just get the energy out you put in.
That's what I used to assume as well. It isn't accurate though. If the water that comes back to the heating element is too hot it'll not be as efficient as when the temperate is lower. Similarly, the additional energy that's needed to heat the water to e.g. 75+ degrees Celsius is wasteful. You can save around 30% of the energy by reducing the temperature of the water that's used to heat your home (though might not work due to various considerations). There are loads of other things that are possible which also significantly reduce the energy usage.
Regarding how to save energy when using a boiler there's a huge Dutch topic about it with loads of tips: https://gathering.tweakers.net/forum/list_messages/2027810. I assume similar information can be found in other languages, though heating using gas and water is really popular in NL (more so than any other country I assume).
> energy needed to heat water to 75+℃ is wasteful. You can save around 30% by reducing water temperature to heat your home
That depends. For resistive electric it shouldn't make a difference, pretty much all heat is transported.
For non-condensing gas (or wood etc.), if your heater is going full blast and a lot of the heat goes up your chimney and lowering the temperature makes a smaller, slower flame, that gets absorbed better, I think you could get 10-30% difference. The heating of water itself to 20℃, 75℃ or 110℃ shouldn't make much of difference, as you're not supposed to cool the effluents too much, or you get condensation, acids, rust ... which will likely kill you equipment.
Condensing gas is cool, extracting so much heat, that water condenses, but the gas must be clean enough and the condenser resistant to corrosion. Here, lowering water temperature can safely lower the effluent gas temperature for more heat extraction (even in optimal power range), and condensation of resulting water vapor from burning gas is about 10% extra energy that would otherwise go up the chimney. I'd expect about 15-30% more heat than non-condensing, especially if run on lower temperatures.
Heat pumps are quite efficient at moving heat, where 1W of electricity can move 3W of heat for a 4W heating yield. A steeper gradient means more work, so pumping heat from 20℃ to 75℃, 1W may only move 0.5W of heat for 1.5W yield (numbers not accurate). Lowering the temperature can make a 2x difference, or even more in extreme cases.
I wouldn't be too trusting of the claims of a manufacturer who's main selling point is the savings in energy...
They might still be true though, but if you keep in mind that it takes about 5 times more energy to evaporate water than to heat it to 100C, and that heating water is more difficult than most other substances it is really not clear why using more heat would be (far) less efficient. Sure it would consume heat at a higher rate, but also less long.
Edit: Also it's not that using lower-temperature water to convey heat is somehow more efficient, the thing with heat pumps is that they are more efficient at heating things to a lower temperature. If you're burning gas it doesn't really matter either way, you just get the energy out you put in.