SaturnV,
Tim Vasquez's paper is indeed an impressive document. As I don't have to remind you, he did not entirely rule out the possibility of what he calls a "Warm sink" by the northern face of that Cb, which I guess marks the "front" of what the French still call le "Front Inter-Tropique". I suppose that this warm sink would amount to a downward kink in the tropopause. And we all know what flying in and out of the "trop" can be like.
The increase in SAT would lower the Mach for a given TAS. The wind would change, and the BEA commented that there was a weak jetstream of 280/85 at latitude 10N to the west of track. This MIGHT indicate a switch from very light headwind to a tailwind on the north side of the ITCZ. The downdraft also might cause loss of performance. The engine thrust would be lower for a given N1. Turbulence would be inevitable. The combination of all these factorss might present significant handling problems, even without the loss of reliable IAS/Mach indications.
Vasquez's flight-profile suffers slightly from lack of available data: I refer particularly to the isotherms, which he had to draw perfectly horizontal. Interestingly, the altitude scale is for true altitudes, and he shows AF447 at 35000ft on the -43C isotherm. On his modified SKEW-T for the "most probable" case (Fig 11), he has substituted a true altitude scale for the scale of pressure (millibars) on the vertical axis. The diagonal isothermic lines show -43C as being at about 37000ft, which I interpret as being the true altitude at FL350 (due to the ISA deviation).
If you suddenly encounter even warmer air (albeit only affecting the higher levels – not the whole atmosphere below you), you need to climb even higher to maintain FL350...
Chris