Controlling your heating and/or cooling system
To make a working thermostat, you will need some way to let it control the temperature in your house. One way to approach this is to let an Arduino replace your existing thermostat and have it control the HVAC (heating, ventilation and/or air conditioning) system in your house in the same way the thermostat did. Alternatively, you could have your network control mains power to a device, such as an electrical heater or standalone air conditioning unit, and control the room temperature through that.
Ideally, you could toggle heating or cooling for each room in your house separately. Combined with a temperature sensor in each room, you would have detailed control over the temperature in every room of your house.
For simplicity, these examples assume that you will control the heating using a single on/off switch for the entire house. If you (instead or additionally) want to control cooling, the examples will be easy to modify. If you have a way to...