The answer depends on what kinds of microorganisms you want to kill. (There is stuff growing in the virtually-boiling geysers at Yellowstone.)
When I am high in the mountains, about the only organism that I feel the need to kill is giardia lamblia. It has a kill temperature of 175 F. So, at any reasonable elevations, just bringing your water up to boiling at 190-210 will kill it.
Now, there could conceivably be some bacteria and virus problems, but not where I've been hiking. Nearly everything will be killed by the same boiling temperatures.
If you go up to 20,000 feet elevation, this rule of thumb no longer applies. As I recall, the 175 F boiling point is reached around 19,500 feet.