The part of the brain that regulates body temperature, hunger, and water balance is A. Hypothalamus.
Hypothalamus: This region of the brain is crucial for maintaining homeostasis in the body. It regulates body temperature through mechanisms such as sweating or shivering, controls hunger and satiety (fullness), and monitors and adjusts water balance.
Infundibulum: This is a stalk-like structure that connects the hypothalamus to the pituitary gland, but it does not regulate these functions directly.
Medulla oblongata and Pons varoli are parts of the brainstem that are involved in regulating basic physiological functions such as breathing, heartbeat, and reflexes, but they do not primarily regulate body temperature, hunger, or water balance.
Therefore, the correct answer is A. Hypothalamus.