I have a cheaper thermostat with wifi, a few months ago it alerted me that the temperature had been more than 5 degrees over setpoint for half an hour and something was probably broken. I was able to remotely shut off the unit and after I came home from work, sure enough the coils had iced over due to a refrigerant leak.

It was only hot enough for this to happen at the peak of the heat when I was at work. I was able to catch the problem early and fix it cheaply all for the cost of a thermostat (Emerson Sensi) about $40 more than a non wifi model.