Other than geofencing, they can "learn" and auto-adjust to increase efficiency. It's been stated installing a smart thermometer can save up to 25% on your bill and with them now being relatively more affordable (~ $150) seems like it would be worth it if for no other reason than to get rid of the old mercury switch types at least when it comes to heating.
I don't have a heat pump.
I constantly get emails from solar companies looking to install panels on my house to "reduce your dependency on the electric company and save money each month." Where we live
it is very sunny nearly year round (229 days with sun) so yeah the panels would probably work great. Our house faces the North, back to the south. Perfect there too. I give my electric bills to them just showing what the usage has been...not the cost. They come back with a $30k system, great! Just one small problem, the monthly payments on the system alone will cost more than what our monthly cost is for electricity. Plus the wife doesn't want anything on our two year old roof (don't even think about install on the ground)...and neither do I. Happy spouse, happy house.
Then there's the annual maintenance requirement as well.
If you need hot water during the day you can jack up the temperature it heats to when costs are lowest.
This is a terrible idea IMHO. Hot water heaters, though they can be set to 140, should NEVER be set much higher than 120. @120 scalding occurs in 5 minutes give or take, at 140 it's like 5 seconds.
The most common regulatory standard for the maximum temperature of water delivered by residential water heaters to the tap is 120 degrees Fahrenheit/48 degrees Celsius. At this temperature, the skin of adults requires an average of five minutes of exposure for a full thickness burn to occur. When the temperature of a hot liquid is increased to 140o F/60o C it takes only five seconds or less for a serious burn to occur1. Coffee, tea, hot chocolate and other hot beverages are usually served at 160 to 180o F /71-82o C, resulting in almost instantaneous burns that will require surgery. Since immediate removal of the hot liquid from the skin may lessen severity, splash and spill burns may not be as deep as burns suffered in a bathtub.
As an aside our windows have a reflective coating on them. During the summer very little heat is transferred into the house through them.
There generally isn't a "one size fits all" when it comes to trying to save energy. Most, if not all, electric companies will perform an energy audit for gratis, or a small fee, if asked.