Definitely does not work with the Nest. I'll see what inexpensive smart thermostat I can get.
Any similar but less expensive alternative that would also work?
At one point in the far distant past I had a CT100 that worked with the Generic Zwave driver.
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I went through the entire zwave thermostat compatibility list and all are not available anymore or are ridiculously expensive. Going through the zigbee list now.
Want to buy a used GoControl Z-Wave thermostat (GC-TBZ48) from me? Contact me directly.
It worked fine with Hubitat; I removed it when I switched to a 3-zone heating system.
Battery powered so you could mount it anywhere.
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You can simulate a connecttion to the HVAC by adding a resistor (1K or so) say, between RC and W terminals. This should simulate heat only mode.
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Zigbee smart thermostat.... cheap and battery powered. Not pretty but it works. Also is a full-featured thermostat, not "heat only" as the link implies.
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Does that mean the thermostat wouldn't allow me to change the AC and Heat settings?
I don't know the answer without trying. But add a second resistor between RC and Y terminals for simulating "Cooling" as well (two resistors should do the trick but maybe just one is enough).
I just bought a couple of T6 Pros off of Facebook for 75 bucks for both.
People buy a house and don't like them.
An update: I only had 75 Ohm resistors in the house. Connected up the C and Rh wires from the HVAC and put a resistor between Rh and W. Nest showed that I have a heating system connected! Put a resistor between Rh and Y and then it showed I have a cooling system. All great! It let me set up the thermostat.
Well, until I put it into heat mode. The resistor burned a bright orange and charred the base and back of the thermostat until I yanked the whole thing out. Thankfully, the thermostat still works and there is no charring on the wall. Only a smell in the air.
1K resistors on their way! I should have called Patience Man earlier. 
Make sure the resistors are big enough to handle the current (power).
They may get warm but shouldn't get HOT and burn up.
Ohms law... P=E^2/R or 24^2/1E3 (1000). about 1/2watt.
Usually the transformer in HVAC air handlers output about 27VAC RMS though, so a 1 watt resistor would be big enough.
75 ohm would be almost 10 watts!!!! oui!
Also, the heat generated by the resistors will affect the thermostat's reading if they are close to the stat, so make sure they cannot "heat" the air the stat is sensing.
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Ops, I am sorry, I forgot to mention power dissipation because this is so obvious for my EE brain. The resistor value could be much higher (will dissipate less power) but without experimenting it is hard to say how high it can go. All what Thermostat is loking for - is a presence of 24V AC on the heat/cool/fan terminals when circuit is not active. This way it knows what exactly is connected.
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The Eecobee stats do the same thing... They look for the load on the output terminals to configure the modes.
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Yeah, I did the calculations AFTER 
the burnout and came to the same conclusion!
Update 2: The Nest doesn't even need resistors. Patience Man hadn't arrived yet! Prepping for arrival of resistors, I just inserted 2 inch wires into W and Y and the Nest thinks there is an AC and Heating systems installed. The other end of each of the wires isn't connect to anything! 
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Hard to believe but it is what it is. If it picks a noise (wire is acting as antenna) this could be very unreliable status reporting. But from the other side this tells me the resistor value could be much higher. Say, even 100K resistor should be OK.
Me being me, I took it a step further for fun. I removed the Y dummy wire -> the thermostat recognized an equipment change that there is no cooling system. Then I hacked the Y connector to be (de)pressed when the thermostat gets attached to the base. Guess what? The Nest recognized a cooling system!
I connected the wire normally so there is no risk of the hack from falling out in the future. Looked for thermostat teardowns, but couldn't find one where the connectors are opened. So, my guess is some tiny contact switch that closes when the connector is depressed.
According to your test it looks like this is a case. But me being EE never will be design system this way. Electronic sensor is basically comes for free with near all modern microcontrollers. Electronic sensor can actually monitor system on a fly and report a real problem when it happens. This mechanical switch (or whatever it is) helps to automatically figure out system configuration but will miss a real potential problem with HVAC equipment.
Anyway, in your case you can fake the Nest just by inserting a little piece of wire.
I am sorry, I did not warn you about potential problem with overheating a resistor.
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Don't be sorry. I'm glad it's in this thread for others in the future. I should have known better anyway. The upside is that impatience led me to learn that no resistor is required at all!
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Well that is even BETTER! Don't need to worry about a resistor(s) heating up and fooling the stat!
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