The efficiency thing is more about heat engines. When we're just dissipating heat, the relevant relationship is that the rate of heat transfer is proportional to the temperature difference. This is why a hot object that isn't producing heat will cool exponentially. In the case of a steady-state source of heat, the temperature difference will be inversely proportional to the thermal conductivity of the connection between hot and cold reservoirs. Heatsinks and fans are used to increase that thermal conductivity so that the temperature difference stays small enough that the absolute temperature is safe. If you can double the tolerable temperature difference, then you can cut your fan speeds by more than half, or even get by with passive convection.
Or, approaching things differently, if you're only going to keep your graphics card for two or three years, there's no reason to let the fans spin up to an audible level until the chip reaches at least 80 degrees C.
Addressing a common misconception: fan speed/noise is not directly related to how much the graphics card is heating up the room by. Whether you run the fans at full tilt or you let the chip almost melt, the heat output will depend only on the workload.