How does air temperture aloft vary with latitude ?

[wiggy]

Don't forget the Tropopause.

I think the environmental lapse rate is generally quoted as being approximately 2 Celsius per thousand feet, as per DR and Tarqs posts. However don't forget (?) the Tropopause, the point at which the temperature stops dropping or sometimes even begins to start rising again as you continue to climb, and which tends to be at lower altitudes over the poles than over the equator..it can certainly be well below 38,000 feet at higher latitudes, indeed down in the 20 thousands of feet is quite common. As a result linear extrapolation of temperature might work up to 38000 feet at Equatorial Latitudes where there's usually a very high "Trop", it won't be valid near the Poles.

In the real world I can't recall seeing much colder than -65 to -75'ish celsius.....that's over Siberia cruising in the mid 30 thousands of feet.

BTW as far as I recall it the wet/dry diabetic lapse rates (1.5 and 3 degrees per thousand) are much more tied in with stability/instability and apply to ascending masses of air, rather than the linear drop in air temperature as you yourself ascend through the atmosphere.