I use intelligence mostly just as perspective of analysis to a system. E.g. Can it be seen to process information? How complicated is the transform from the information to some action? Does the processing lead to some good outcome, e.g. self-preservation of the system? Could the information processing be improved for this outcome?
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.
The broad definition is not justified by the fact that certain attempts to define the term would attribute intelligence to thermostats; a more useful conclusion to draw is that the definitions in question could be improved.
It is sometimes said that we won't be able to gain an understanding of intelligence until we have a precise definition, but it's actually the other way round: definitions get tighter as our understanding increases. We now understand many things that not only were lacking definitions in the past, but were not even imagined.