A cooling system for use in with a transmissive optical element of a high average power laser (HAP). The system includes at least one optically transmissive element (TOC) that is held by a differential pressure in thermal contact with a heat sink assembly. In one embodiment, the heat sink assembly includes an optically transparent heat conductor (THC) attached to at least one face of the TOC. A vacuum formed between adjacent faces of the TOC and THC urges the facing planar surfaces into thermal contact with one another. Waste heat generated in the TOC is conducted to the THC. The temperature gradient inside the TOC is maintained substantially parallel to the direction of a laser beam being directed through the THC so that a given phase front of the beam exposes TOC material to the same temperature. As a result, the TOC does not perturb the phase front of the laser beam.