Step 1: Temperature homeostasis is a hypothalamic function. Among the hypothalamic nuclei, the one that senses and sets core body temperature is the preoptic nucleus of the anterior hypothalamus.
Step 2: Warm-sensitive neurons here increase their firing when blood temperature rises, switching on cooling mechanisms (sweating, vasodilation). When temperature falls, the posterior hypothalamus drives warming mechanisms (shivering, vasoconstriction).
Step 3: Eliminate the wrong options: supraoptic and paraventricular nuclei are neuroendocrine (ADH, oxytocin), and the suprachiasmatic nucleus governs the sleep-wake circadian rhythm, not thermoregulation.
\[\boxed{Preoptic\ nucleus\ of\ hypothalamus}\]