Assuming you don't have a smart thermostat, I'd also suggest using your WIFI router's mobile app to check power status. I have Nest thermostats and a Nest Router, and in my experience I only lose internet connectivity if my power fails. Also signing up for SMS alerts from your power co is good but sometimes they are very late.

Of course if you have a smart thermostat, you can have an alert set for when the temp dips below an acceptable limit, which would indicate heating system failure.