It isn't the mental state which modifies behavior
Myself, I would say it is the mental state which actually carries out the modification in behavior. Although hunger is underpinned by a biological process which affects the brain, I think it's only when that effect on the brain enters into your mental awareness (either consciously or unconsciously — because we can also be unconsciously aware of many things) that behavior can be modified.
As my working definition, the mind corresponds to (and integrates) the areas of the brain that we can become consciously aware of. For example, if you have an itch or pain in your foot, that info is transmitted to the brain, and then as the next step, enters into conscious or unconscious awareness (your mind). You may as a result, either consciously or unconsciously, scratch your foot.
Thus if any of areas of the brain that we can become consciously aware of are altered by some physical biological process such as a hunger hormone, then it will in turn enter the mind. But if a biological process alters some part of the brain that we can never become consciously aware of, then it will never enter the mind.
An example of a biological process affects the brain, but does
not enter into the mind is the control of blood pressure by the medulla oblongata in the brainstem. This part of the brain receives information about the current blood pressure level from various baroreceptors in the body, and then in response sends outputs to the body in order to control and maintain blood pressure. But we are entirely unaware of this biological process in the brain, because although it enters the brain, it never enters into the mind. Thus not everything that enters the brain enters the mind.
So generally speaking, I think a biological process that affects the brain can only modify behavior if it enters the mind (by which I mean it enters into conscious or unconscious awareness).
The only counter-example I can think of, where a biological process affects the brain, and may alter behavior
without entering the mind, is pheromones (pheromones are chemicals in the air which we can detect with a special organ, but which we are not aware of).