Aluminum better runtime than SS or Ti?

With all things being the same on a flashlight except the body material, would an aluminum light give better runtime than one in stainless steel or titanium?

Just wondering how much the heat buildup to LED and driver from SS or Ti can affect runtime.

For example, I would love to see a runtime of two Quark MiNi's on high, one in Al, one in Ti just to see how much of a difference the runtimes would be.

Doesn't have to be a MiNi could be any light that comes in both flavors.

Any input is greatly appreciated!

I doubt that the effect would be measurable.
Aluminium would better disipate heat and might therefore give a very slightly brighter light since LEDs are more efficient at lower temperatures.
As regards run time, I would expect that the battery current and therefore the run time would be unaltered.
There might be minute differences if the losses in the driver circuit varied with temperature, but probably too small to measure, and also probably smaller the the variations in battery capacity from one charge cycle to the next.