Zinc oxide is used in some TIMs, for example, Zalman thermal grease ZM-TG2 the effective ingredient is zinc oxide. Zinc oxide has a thermal conductivity of 1.2 w/mk, and that is what is listed spec for Zalman thermal grease ZM-TG2. Compare that to aluminum oxide based 2x thermal cond., or some of the more modern TIMS that have 4-5x higher conductivity and lower contact resistance.
So Zinc Oxide is a mediocre performing thermal interface material.
If using sunscreen for source of zinc oxide however, it wont be formulated for its intended use, wont resist pump out between block and cpu, and though probably perform better than toothpaste at first, will likely degrade quickly over time.