A number of systems are now on sale in the UK, and they promise big savings.
One being launched this month claims it can save you as much as £400 a year on your energy bill.
Certainly the internet giant Google seems to have recognised the potential for the technology, having just snapped up the US manufacturer Nest for about £2bn.
But how real are the savings, and who could benefit?
All these systems work by maximising the time your heating is switched off.  And switching it on only when you need it.
So think of the last time you went out for the evening and left your heating on. Or got home late from work.
Or maybe you did not need the hot water, having showered at the swimming pool.
But many of these devices are far more sophisticated than simply switching your heating off and on remotely.
Using GPS technology, phones now know exactly where you are, and using that knowledge, systems can anticipate when you are likely to get home.
So when Will Moore begins his journey home from London to Kent, his boiler in effect tracks his progress, and makes sure the house is up to temperature only at the moment he walks through the door.
It will even take account of the local weather forecast, and adjust itself according to expected temperatures.
He paid £250 to have the system installed two months ago, but he has already noticed the savings.
"It's saving us, I think, about 20% to 30%," he told the BBC.
"Based on that it should pay for itself within about three years."
Tado, the German manufacturer, claims savings of up to 27% on annual bills.
If you are prepared to pay a little more, the potential savings can be even bigger.
First, think of the times of day that rooms are heated unnecessarily in your home.
Is the heat blasting out in your sitting room at six in the morning, when no-one will actually sit in there until six in the evening?
Is your bedroom cosy and warm at 19:00, just when you are in the kitchen having dinner?
For around £850 for a three-bedroom house, you can install a system that will allow you to heat each room individually.
Using your smartphone, or a central control panel, you can work out temperature profiles for every room in the house, and of course adjust them from anywhere in the world, providing there is an internet signal.
Honeywell, which makes the hardware in Scotland, claims you can save up to £400 a year on your energy bill by "zoning" your home in this way.
And it says the system should pay for itself in two or three years.
So how realistic are the savings claims being made?
The answer will depend on the size of your house, your lifestyle, and the energy-saving measures you have already taken.
Those with large houses can certainly save more.
Stephen Passmore, from the independent charity the Energy Saving Trust, is enthusiastic about the whole concept, but warns that those in small flats will probably see little benefit.
"Comparing someone who lives in a large detached property to someone in a one-bedroom flat, the person in the larger property could obviously have a much larger potential saving," he says.
And he points out that basic energy-saving measures can save you just as much, if you have not already had them installed.
Eight million people in the UK do not yet have a thermostat, for example, which can save £65 a year alone.  Among other money-saving measures, he recommends:
Your lifestyle too will make a difference. Those without children, or who come home at unpredictable times, may have a greater potential to make savings than others.
"It remains to be seen whether they offer a net benefit financially," says Thomas Lyon of the comparison site uswitch.
"But they will appeal to some customers, particularly as energy efficiency becomes even more important in keeping bills low," he adds.
British Gas has already launched its service, known as Hive, which claims to save customers up to £150 a year.
Scottish Power and Honeywell are due to launch their systems later this month.
Have you ever thought about using a smartphone to control your central heating?