Yes that is how they work. They heat the filiment to a certain temp, then it measures the voltage that it takes to keep it at that temp. The more air that flows across it, the more it takes to keep it up to temp. The PCM converts the voltage into airflow across it and compensates fuel and timing for it.
But they also have a barometric pressure sensor in them too. Mine failed under warranty and it caused a lean condition.
You may try a local salvage yard for a good used one. Just make sure that it has the same part number as yours so that it will be calibrated the same.