The warm cup will have a faster reaction because heat is a form of energy, and energy increases molecular motion. When the molecular motion of the water is increase due to heat, the pull that the water molecules exert on the molecules of the pill will increase increasing dissolution.
It is worth pointing out that different substances have different properties like ions, molecular structure, etc. Therefore, the extent to which the heat will increase the dissolution will vary depending on the substance. In this case, antacid medication usually contains sodium bicarbonate. The cup filled with warm water will have a faster reaction because heat, as stated before, increases the molecular motion, which increases the chances that bicarbonate ions are exposed to the hydrogen ions.