Do you understand what crictal altitude is.
Next I take it that no combustion engines work at altitude and in cold weather. That's strange I've worked at above 10000feet and we had Diesel engines working.
As for cooling yes they work better in general the hotter they get. This is also overcome with engineering. It's easier to heat an engine than to make it cooler. So still what is the crictal altitude for a complete turbo failure and to loose all performance from the engine. Next what is the crictal altitude for a normal ignition engine for a restart.
Even most turbines can't be started above 10000 feet. Your argument dose not stand up for restarting.