Thermostat wire will be cheaper than the wire near it on home-improvement shelves because it is smaller — it does not carry high current or high voltage in the intended application, so it does not need to be thick or have strong insulation.
This, in itself, is fine for HF antennas — except in high-power applications, the current is not a problem, and the voltage is better addressed by distance than by insulation.
However, it is probably solid wire. Solid wire is not a good choice for portable wire antennas because repeated bending will fatigue and break the copper. (It's okay to use solid wire for a self-supporting rigid antenna such as is found in VHF and higher frequencies, though copper is a bit soft for that application.)
You should look for stranded wire for building antennas if you want them to last.