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No it is simple feedback device unless it is programable thermostat.
Suppose it's programmable.
Then yes, it is a computer. I think a more natural way of speaking would be to say that it has a computer in it.
Well, no; it has an embedded chip...that doesn't make it a computer, does it?
We have to start with definition. To most people 'computer' means personal computer and even if thet think about supercomputer they see more powerful pc. If we however stick to the definition 'device that process data' than computer will have much broader meaning. ENIAC was a computer but it did not resemble present computers. Computer computes data therefore any device that does it can be called computer. Programable thermostat has small computer inside and one of the more sophisticated might be more powerful than ENIAC.
A computer used to mean a person that computed, eventually a person that computed using an adding machine. Many of these computers were women. The computations were often systems of differential equations (or other linear systems), for example, solving problems in ballistics.