I would be surprised if any wx engine for FSX/P3D bothered with a bulging atmosphere a the equator. I should be using the term tropopause, which is where the troposphere ends and temperature lapse rate ends.  Thermocline is for water doh.  At the equator is is about 59000 ft, at the poles about 26000 ft. Quite a bulge I would say.

I fcind it hard to understand why the air would be colder over the equator.  Consider the tropopause....this is where the aidiabatic lapse rate turns positive. also think about the surface temperature which at the surface will be higher at the equator.

The lapse rate is consant to the tropoause so even if this was higher we are starting at a higher initial temperature so at if the surface temperature is 40 degrees the temp at 30 000 ft will be only minus 20 and this assumes the troposphere is at 30000 ft (unlikely)

At high latitudes we are unlikey to be this warm.

 

 

The lapse rate is consant to the tropoause so even if this was higher we are starting at a higher initial temperature so at if the surface temperature is 40 degrees the temp at 30 000 ft will be only minus 20 and this assumes the troposphere is at 30000 ft (unlikely)
At high latitudes we are unlikey to be this warm.

You assume a linear temperature lapse rate based on temp, across all latitudes. This is not accurate, your graph, while good, is an approximation. Generally, over the Equator, the temperatures can very easily be similar or colder than, the far North or South.

 

Also, 40degC is high, even for the tropics. 30degC would be a more normal temperature.

 

This has a good explanation:

 

https://www.quora.com/Why-is-the-temperature-on-the-tropopause-more-at-the-poles-than-the-equator