Not an expert, but have some layman experience from flashlights. Assuming handheld laser. I think it depends on if the host can radiate all of the heat heat produced in to the air and into your hand. If it can, conductivity/emissivity are most important. If it can't, then finding a way to increase storage capacity would be more important to extending run time. In flashlight, I try to get the most of both so that I can run the light continuously at the lower and maybe mid level modes, but also have the ability to run at a crazy high level for bursts.
I don't know the formulas for types of materials, finishes, surface area, etc to determine how much heat a particular host can shed into the air and your hand.