Saying that a thermostat with a servomechanism is self-aware is just repeating the same broadening-beyond-usefulness with a different (though related) concept, in this case self-awareness. The difference between the self-awareness of humans and that which you see in a thermostat is vast, and understanding how a thermostat works gives no useful insight into how the human mind works.

Any system processes information, and in a thermostat it is not complicated at all. Even the most self-aware thermostats currently being manufactured are not going to improve themselves on their own volition. Applying the term 'intelligence' this broadly turns it into an empty tautology, or a little piece of uninformative noise on a communications channel, no more useful in understanding those systems than in understanding actual intelligence.