Coilcraft’s app note on temperature rise due to losses on inductors and transformers. Link here (PDF)
Core and winding losses in inductors and transformers cause a temperature rise whenever current flows through a winding. These losses are limited either by the allowed total loss for the application (power budget) or the maximum allowable temperature rise.
For example, many Coilcraft products are designed for an 85°C ambient environment and a 40°C temperature rise implying a maximum part temperature of +125°C. In general, the maximum allowed part temperature is the maximum ambient temperature plus temperature rise. If the losses that result in the maximum allowed part temperature meet the power budget limits, the component is considered acceptable for the application.