A method of making an HID lamp and an HID lamp that includes a ceramic envelope with a ceramic capillary, wherein the capillary has an electrode feed-through therein that is sealed inside the capillary by a frit seal that extends inside the capillary a first distance from a distal end of the capillary, and a ceramic heat sink around at least half an external diameter of the capillary, wherein the heat sink is separated from the envelope and from the distal end of the capillary and the heat sink is in thermally conductive contact with the capillary and has an external diameter at least 1.5 times the external diameter of the capillary. In one preferred embodiment, the heat sink does not overlap the frit seal.