In a light emitting package (8), at least one light emitting chip (12, 14, 16, 18) is supported by a board (10). A light transmissive encapsulant (30) is disposed over the at least one light emitting chip and over a footprint area (32) of the board. A light transmissive generally conformal shell (40) is disposed over the encapsulant and has an inner surface (44) spaced apart by an air gap (G) from, and generally conformal with, an outer surface (34) of the encapsulant. At least one phosphor (50) is disposed on or embedded in the conformal shell to output converted light responsive to irradiation by the at least one light emitting chip. A thermally conductive filler material disposed in the generally conformal shell (40) is effective to enhance a thermal conductivity of the composite shell material to a value higher than 0.3 W/(m·K).