We have a heat pump, so we change the temperature roughly twice a year: heating temperature in winter, air conditioning temperature in summer.
But my Ecobee reports the temperature in three rooms (and occupancy, which I tie into automating lights), outside temperature, outside and inside humidity, fan/heat/cool start/stop times, and some other more obscure metrics up to the mothership, and the excellent third-party website Beestat[1] tracks all of those using Ecobee's well-documented API. It lets me spot anomalies, and helps me understand if I've got the resistive heating configured to come on at the best time.
If we had time-of-day rates for electricity, it would optimize for those, but we don't have time-of-day-rates.
(If I had gas heat, or if I didn't work from home, I'd at least schedule temperature changes to set things cooler at night or when we're away -- maybe driven by the occupancy sensors! -- but apparently that's not effective with heat pumps.