The problem revolves around dynamic and static addresses with the internet, to connect to some thing as and when required it needs to have a static address, but most homes have a dynamic address, so your phone tells a computer with a static address what you want, and your home asked the computer with the static address what to do.
At home you don't have that problem, your local area network is static in the main so your PC can connect to your thermostat direct, however quite often you have a mini computer called a hub which relays the information and stores it.
So question one is of course what do you want to do? Or what is wrong with what you have?
Test one with any home before fitting automation is to find out how the installed system will cope. If the heating can raise the house temperature from 16°C to 20°C in 30 minutes and you live 35 minutes from work, then having the smart phone tell the controls you are now 30 miles from home not 40 miles so switch on heating will likely mean you arrive home to a warm house.
However if it takes 3 hours to heat house from 16°C to 20°C then that is for most pointless as we don't work 3 hours away from home.
Next is cooling, if after switching off heating the house will cool 20°C to 16°C in 2 hours then clearly maintaining the house at a lower temperature when away makes a lot of sense. However mothers house the existing programmer switches off heating at 10 pm and by 6 am when I want it back on it has rarely cooled from 20°C to 18°C so question is if worth switching on.
With a condensate boiler there is not a fixed flame height nor is there a fixed efficiency, in the main if a 8 to 28 kW hour boiler is running at 12 kW output it is more efficient than when running with a 28 kW output so in some cases it actually costs more to switch off and on than to leave running.
There are however some ways of saving power, one is not to heat unused rooms, if you only use your bedroom from 11 pm to 6 am then one may be able to save power by turning off the heating at 5:30 am then turning it on at 9 pm to warm the room to 20°C for you to retire, then let it cool to 17°C overnight cause can't sleep if room too hot, then start heating it up again at 4:30 am ready for when you get up. Since you will be sleeping having to wake up and adjust heat with phone is rather pointless, all it needs is a simple timer.
So repeat this with other rooms, maybe you never walk into living room in morning and that could stay cool until 4 pm before it starts to warm up ready for your return at 6 pm then can go off again at 11 pm. Each room likely different, so each room needs it's own controller, you could with something like EvoHome integrate the whole house and be able to control every room independently, however most of us live are reasonable regular life and EvoHome is very expensive.
So stand alone electronic programmable thermostatic radiator valve will likely cost around £24 each, no internet, no link to phone, just controls each room. OK there are some down sides, but also some gains, one is they will allow the boiler to run as intended with a variable output not simple on/off, OK I know Nest has OpenTherm so if the boiler also has OpenTherm it too can turn boiler up/down rather than on/off, however unless boiler has OpenTherm that will not work.
Many of the home so called Smart thermostats are a compromise anyway, even if they can link to the radiator valve they only use IFTTT so don't work by saying does any room need heat if yes boiler runs in not then boiler stops, even with IFTTT link they will only work if every room same temperature, and are a bit hit and miss, only something like EvoHome will really allow each room to have a different temperature and program as to when it needs to be warm.
Some of the systems which seem to allow the same as EvoHome, when you read carefully still only monitor the temperature in one room. There are building management systems, but they make EvoHome look cheap. Same with electronic thermostatic radiator valves, you could use fan assisted radiators instead, they heat the room up far faster, and have far better control, they alter fan speed to adjust heat output and can even be linked to air conditioning for the summer. But once you see the price, think you may settle for standard radiator.
My first house had hot air gas fired central heating, and a single thermostat could control the whole house, you could adjust individual rooms to some extent by moving the louvred vents in the wall, the vents in every door mean sound travelled and the system leaked so cost a fortune to run. This would have worked great with Hive or Nest, and it seems most home in USA have hot air heating. So there are exceptions, but most British homes either simple programmable thermostatic radiator valves, or go whole hog and use EvoHome.
Why do I say this, well because I tried to be clever and got Energenie thermostatic radiator valves, the valves to be fair work well, but as to picking up phone and adjusting the heat in each room, just too slow to respond, so now run simply on time, and for that I could have bought heads at less than half the price.