Simple procedures for designing small, naturally cooled inductors and transformers for high-frequency operation have been developed that are based on limiting the maximum temperature in the components. The physical basis of the procedure is easy to understand, and the procedures progresses sequentially in a series of steps from the assembly of the design inputs to the final design without any confusing iterations. The use of an interactive core database stored on a computer allows the database to be accurately specialized to the particular application under consideration so that confusing iterative searches of static multiparameter databases used in older design procedures are unnecessary. Experimental measurements indicate that the key pan of the design procedure, relating the allowable current density in the windings and allowable flux density in the core to heat loss controlled by radiative and convective heat transfer, is valid. Calculated surface-to-ambient thermal resistances based on these two mechanisms correlate well with experimental values. The introduction of these design approaches in undergraduate courses in power electronics have made the design of magnetic components much easier for students to learn compared to other methods.