I am a PPL student and working on the cross-country planning. Let's say the OAT is -13º @ 6000', how to calculate the OAT @ 7000'?
The temperature will drop around 2° Celsius (-1.98 to be more precise) for each 1000 feet you climb.
So if the OAT at 6000ft is -13°C, at 7000ft it will be -15°C, or minus 16 from the International Standard Atmosphere (ISA) which should be +1°C (15 - 2*7 = 1).
While the ISA lapse rate, normally 3.5F or 2C per 1000 ft is a good ISA approximation, one must keep in mind that fronts, inversions and other weather related phenomena may alter temperatures from the normal lapse rates.
If you are attempting to make accurate estimates of temperatures, while you can apply standard lapse rates, I would encourage you to examine winds aloft, in necessary interpolating the temperatures between forecast points. Then one would interpolate using the forecast winds aloft temperatures.
Looking at a local winds aloft forecast, I see: 3000 2914-05 6000 2820-06 9000 2727-17
So from 3000 to 6000 the forecast is much less than the lapse rate, but from 6000 to 9000, the forecast is greater than the standard lapse rate of 2C/1000ft * 3000ft = 6C but the forecast difference is 11C. So if one were to estimate the temperature at 8000 for this area, I would use: -06C for 6000, minus 2000ft/3000ft * 11C = -6C - 7.33C or about -13.3C
In contrast with the standard lapse rate, in this instance the calculation would be: -06C - (2 * 2) = 10C
Sometimes the forecast values are substantially different from the standard lapse rate. If temperature were important, I would want to develop the best estimate and use the forecast temps aloft.