Nothing that sophisticated (as documented by others here in this forum!) When I got my Solar installed 5 years ago my journey began. Installed a Pi and connected it to the inverter to monitor the Sun. Its still running today and I have lots of stats on power, energy, temps, in total and for each string of panels (4.5 killer wasps).
After a while, I though I need more, so invested in eMonPi to see more details on house usage and exports to the grid. Now, Im Totally into all things measured.
Back then, with a very troublesome, inefficient Gas ducted heating system and with Gas prices here rising sharply, and with an increasing desire to contribute to preventing climate disaster, I moved my attention to eliminate Gas use at my home. My Gas hot water heater was approaching End of Life so I swapped over to heat pump technology. I had done some research and thought I could make better use of my day time Solar generation. I am now a huge fan (pun intended) of Heat Pumps.
When my Hot water Heat Pump was installed a few years ago, I was always wanting to check it running and to measure if my investment was good, etc … I could scan the house power and Solar generation graphs etc but some times the heat pump operation was ‘hidden’. Then I thought I have the ability to connect some temp sensors to the eMonPi, how could I make use of this.
So I have two sensors connected, one on one side of the heat pump fan, and one on the other. Whenever the unit runs I see a dramatic drop of temp on one side. And it looks like this:
The Sanden Heat Pump is programmed with a blockout timer so I have it set to only come on after 1100am to make best use of my Solar generation. From the graph it ran for about an hour today. It will also come on occasionally for defrost mode once or twice a year, so I can see that happen as well.
The temp differential today (miserable rainy winter day) is not that great, but in the middle of Summer on a 43C day the best place to walk past is the Hot Water ‘heater’. ! 
So just an example of a very simple way (two temp sensors floating near a fan) to monitor something. Sure it would be useful to have specific probes on water temps, power usage, etc etc, maybe one day.
PS I have eliminated all Gas and disconnected Gas meter by the way… pulled out the old furnace and rubbish ducting, and installed … more Heat Pumps, what else !