Are emotions purely physical, or are they part of the soul?
Whenever we experience emotions, it always involves some sort of bodily change. For example, if someone insults you, you get angry. And with that anger comes an increase in your heart rate, blood circulation, and the flow of adrenaline.
These physiological changes are due to the operation of the soul, since the soul is responsible for whatever the body does. To use philosophical jargon, it’s the form of the body. But because the emotional experience necessarily involves a change in the body, the emotion is an operation of the soul that is necessarily joined to bodily organs. Therefore, as St. Thomas Aquinas concludes, an emotion doesn’t belong to the intellective part of the soul (the intellect and will) but to the sensitive part (the part of the soul that animates our bodily powers).
Your question implies there are only two possibilities, but in reality, there is a third. The emotions are powers that belong to the soul, but because they necessarily involve bodily change, they belong to the sensitive part of the soul and not the intellective.