Throughout our planet's lower atmosphere, the troposphere, the higher you go, the colder it gets. Sunlight passes through the atmosphere and strikes the surface of Earth, warming it. The heat from the surface then rises through the atmosphere. The higher you go, the farther from the "heater" you get. After thermal stability in the boundary layer called the tropopause, the stratosphere, which is above the tropopause, warms up from bottom to top. The troposphere rises from ground level to about 16 km (53,000 feet) in altitude. The stratosphere climbs to 50 km (164,000 feet) high, just above the ozone layer.
Things You'll Need
 Calculator
 Map
 Thermometer

Record the temperature and your location's latitude. For the purpose of this exercise, use the global average temperature of 15 degrees C and a position at 45 degrees latitude, halfway between the equator and the pole.

Calculate the temperature at the altitude of your choice in the troposphere. Temperatures in the troposphere drop an average of 6.5 degrees C per kilometer (3.5 degrees F per 1,000 feet) of altitude. Five kilometers up, the temperature would be 15  (5 x 6.5) = 17.5 degrees C. This rough equation remains reasonably accurate up to the tropopause.

Estimate the the temperature at the altitude of your choice in the tropopause. The tropopause maintains a more or less steady temperature from bottom to top at higher latitudes. In fact, the tropopause is in part defined by this thermal stability. The temperatures measure roughly 32 degrees C at 75 degrees latitude, 38 degrees C at 60 degrees latitude and 48 degrees C at 45 degrees latitude. Closer to the equator, the tropopause continues to cool. At 30 degrees latitude, the temperature falls to 60 degrees C at 15 km altitude before starting to rise. At the equator, the temperature hits 68 degrees C around 17 km high before rising. The average temperature of the entire tropopause is a steady 57 degrees C.
The tropopause is coldest over the equator and warmest over the poles because as warm air rises and expands, it sucks up heat energy and cools the atmosphere. The more the air expands, the more it cools the surroundings  and warm air expands more than cold air.

Calculate the temperature at the altitude of your choice in the stratosphere. The temperature rises evenly through this atmospheric layer, on average. As noted in the previous step, your latitude is practical consideration. Real weather conditions, of course, are never so cut and dried. NASA supplies a formula that calculates the expected stratospheric temperature (T in degrees C) given the global average temperature of 57 degrees C at 25 km altitude. The formula is T = 131 + (0.003 * altitude in meters).
References
 Photo Credit lago di como  winter atmosphere image by Raffaele Galbiati from Fotolia.com