Great post OP.
There is a lot to consider with environmental lapse rate, adiabatic lapse rates, etc. in terms of cooling.
Here is a good site:
https://en.wikipedia.org/wiki/Lapse_rate
The rule of thumb is approximately 1.9 degrees of cooling per 1000ft. This is a big deal in helicopter mission planning, especially launching from sea level.
Environmental lapse rate:
The environmental lapse rate (ELR), is the rate of decrease of temperature with altitude in the stationary atmosphere at a given time and location. As an average, the International Civil Aviation Organization (ICAO) defines an international standard atmosphere (ISA) with a temperature lapse rate of 6.49 K/km[16] (3.56 °F or 1.98 °C/1,000 ft) from sea level to 11 km (36,090 ft or 6.8 mi). From 11 km up to 20 km (65,620 ft or 12.4 mi), the constant temperature is −56.5 °C (−69.7 °F), which is the lowest assumed temperature in the ISA. The standard atmosphere contains no moisture. Unlike the idealized ISA, the temperature of the actual atmosphere does not always fall at a uniform rate with height. For example, there can be an inversion layer in which the temperature increases with altitude.