Paper makes a good cup insulator because it is able to reduce the conduction, convection and radiation of heat, according to the Illinois Physics Van of the University of Illinois. All three processes help prevent heat from passing through a cup.
Paper reduces the passage of air through a cup. The wood fibers in the paper trap air and prevent convection, which refers to air moving through and carrying heat with it, according to the Illinois Physics Van.
A thicker paper cup will conduct less heat. Hot liquid inside the cup can transfer heat to the cup by conduction, so a thin cup will feel hot, according to School for Champions. A cardboard holder over the cup help prevent additional heat loss.
Another way heat can be lost is through radiation, which occurs when light waves transfer heat from one place to another. Paper blocks light radiation, and so also prevents heat from passing through a cup.
References and ResourcesUniversity of Illinois: Best thermal insulator
School for Champions: Heat Transfer