Not true. this is a textbook shunt regulator.
You need to size the zenar for worst case case however. At most your resistor can only drop say .3 volts under the full load of the thermostat... which would be what, milliamps?
and therefore at the full 15.5 volts, the resistor will be dropping 3.5 volts, so you might need a 1/2 watt or even a 2 watt zenar, depending on what resistor you choose, and what voltage drop you consider acceptable.
If .5 volts drop is unacceptable then get a dc-dc converter. I don't know of any FET based linear regulators that you can get off the shelf, might try making your own.. but they tend to oscillate. It might be less effort to build a more intelligent thermostat anyway?