The Elgato Eve Thermo isn't a house-wide thermostat - instead it connects to individual heating units and controls them separately instead of single point of interaction. This provides better distribution when heating, as only the rooms that need heating will be heated.
Pro Room-by-room control, scheduling, and heating
Because each Eve Thermo is assigned to a single room, it can accomplish a steadier temperature than a single central thermostat. You can assign each room to a different schedule, for example your bedroom heater can be turned off during the day while the rest of your house receives the heat instead.
Pro Small, sleek looking hardware
The Eve Thermo is physically small, and plugs into your heaters which are usually hidden out of sight. This allows it to discreetly add smart heating to your house without creating an eye-sore on a prominent wall.
If the device is in a location where it will be seen however, it looks very sleek with it's polished white colour and rounded square design.
Con Not a whole-house unit
The Eve Thermo only connects to a single heating element. That means that for your entire house to be heated this way, you'd need one Thermo for every room in your house - at which point it would be much more cost-effective to get a single smart thermostat.
The Eve Thermo is better suited as a complementary device - one that is installed alongside your current (or future) thermostat. The Eve Thermo works very well when it comes to regulating temperature in a tricky room (where a normal thermostat leaves it either too warm or too cold), and that is where it excels.
Con Limited control distance
The Eve Thermo only connects via Bluetooth, and has a short range (~4 meters). You won't be able to adjust the temperature from outside the room, unless you have an Apple TV 3rd gen (the Apple TV hooks up to the Thermo, and allows control through Wi-Fi which can be accessed and adjusted from anywhere in the world with an internet connection).