A light emitting diode (LED) lamp includes a base with one or more LED chips, an internal cover over the LED chips, where the cover is a translucent ceramic whose thermal conductivity is greater than glass, where the cover has an interior surface separated from the LED chips by a gap, and where an exterior surface of the cover is coated with a phosphor. The ceramic cover preferably has a bulk thermal conductivity of at least 5 W/(m·K), such as polycrystalline alumina. The LED chips preferably are blue LEDs and the phosphor is selected so that the lamp emits white light. In the method of making the lamp, the phosphor may be applied to the exterior surface of the cover as a preformed sheet or in a coating.