Sugar dissolves more quickly in hot tea than in iced tea because the solubility of solutes in solvents generally increases with an increase in temperature, according to Rutgers University. The heat provides energy to break the molecular bonds in the solid, causing it to dissolve faster.
This effect of temperature on the solubility of solids is explained using Le Chatelier's Principle. The principle states that if stress, such as heat, is applied to an equilibrium, the system adjusts to minimize the effect of the stress. Therefore, since the breakdown of molecular bonds requires heat, an increase in temperature favors dissolution as the system attempts to remove the added heat.