Tim Vasquez's
weathergraphics.com page contains a lot of information relevant to this discussion. His profile graphic - reproduced below, with modified position timings gives a fairly good representation as to the likely condition of the air-mass.
You'll note that he is using ISA+10°C giving -44°C at FL350. Interpolation / extrapolation of OAT within the mesoscale system is a big variable. Tim quotes tops at 56,000 feet (17,000m), but doesn't see anything out of the ordinary in this ITCZ event. Lightning is also very rare within these marine environment MCS clusters, and none was recorded.
This event is most likely causal to the upset, but the why and how need answers.