How does latitude affect the air temperature at 8 km altitude where planes fly?
In the troposphere, air at altitude is colder than air at ground level. But surprisingly, air at altitude at the poles can be warmer than air at altitude at the equator. From the wiki article on troposphere (I added the bullet points):


  The troposphere is heated from below by latent heat, longwave radiation, and sensible heat. Surplus heating and vertical expansion of the troposphere occurs in the tropics. 
  
  
  At middle latitudes, tropospheric temperatures decrease from an average of 15 °C (59-degree Fahrenheit) at sea level to about −55 °C (-67-degree Fahrenheit) at the tropopause. 
  At the poles, tropospheric temperature only decreases from an average of 0 °C (32-degree Fahrenheit) at sea level to about −45 °C (-49-degree Fahrenheit) at the tropopause. 
  At the equator, tropospheric temperatures decrease from an average of 20 °C (68-degree Fahrenheit) at sea level to about −70 to −75 °C (-94 to -103-degree Fahrenheit) at the tropopause. 
  
  
  The troposphere is thinner at the poles and thicker at the equator. The average thickness of the tropical troposphere is roughly 7 kilometers greater than the average tropospheric thickness at the poles.


There is quite a bit of variation in the troposphere as a function of place on earth, and much effort has been put into creating a standardised atmosphere that can be used for practical purposes around the world. The ICAO standard atmosphere serves that purpose. It cannot account for local wind conditions and humidity.



I found a graph in an old paper format uni book on the atmosphere, depicting average conditions in two separate places on earth, Berlin and 40° latitude in North America. The graph shows that although the temperature lapse rate is very similar in both cases, there is a difference in temperature at a given height. The arrow gives the temperature difference at 8 km height, also transported to 0 m (less average difference) and to 10 km (more average difference).

Above is for average temperature at two different places on earth, at similar latitudes. I could not find any direct comparison between average temperature at altitude of the poles and the equator - the wiki article seems to indicate that average temperature at the poles is higher at high altitude, a surprising indicat