Gotta ask; why pay extra for a wifi thermostat?
Programmable thermostats have proven their savings and Last I looked, only cost around $25.
I don't see any ROI on the extra money spent.
I want 'smart home' devices to control and monitor a few things (to start, with the option to get into home automation), but I can't find any ROI to justify it.
It depends on the system. If you've got cheap natural gas heating, the ROI on a fancier thermostat is limited. If you have something like a heat pump with backup coils (big resistors that consume hellish amounts of power), running the system intelligently is worth something. I'm fairly certain our Nest unit has saved us money in the past year and a half, simply because it tries to run the heat pump intelligently compared to the cheap programmable thermostats. The basic heat pump thermostats are really, really stupid - they'll panic and turn on the backup coils if you ask for more than a few degree difference, even if it's 80F outside (when we got our house installed, I cooked it to drive out the various volatile organics as best I could). The Nest will start the heat pump quite early in the morning to bring the temperature up.
Plus, a lot of the smarter units (vs a simple programmable) are better at detecting (via motion sensors, phone location, etc) if someone is home, and if not, they'll open up to a much wider temperature range. Our thermostat is set to one range if people are home, but if nobody is home, it lets the temperature range from something like 50F to 90F (I'd set it higher but we have ferrets and they don't do well at high temperatures, though they love the cold). This is automatic - we don't have to think about it. Or we can set it away from a phone. Or, on our way home from a weekend out camping, tell it to start actually doing something as we head home, and have the house reasonable when we get home.
The Nest will also run a dual fuel system reasonably - if you have a heat pump with a natural gas backup furnace (in place of the coils).
Now, I think most of the "Smart Home" gizmos are worthless gimmickry. Alexa included. But with typical home climate control energy use, they can be a lot more efficient than just a basic programmable.
True badassity would have been simply connecting together the thermostat wires to get heat as needed until you had time to do a cost/benefit analysis of programmable vs wifi thermostats, and then shopped for the best deal.
That was my first thought as well... look up a wiring diagram for whatever my furnace configuration was and hotwire the furnace with a toggle switch or something until I got around to fixing it. :)