If you measure those negligible few degrees C you're talking about in degrees F (like they do with flights out of America), then the temperature difference is a lot more.
That conversion makes a big difference.
The same type of error led to the loss of an European Mars lander a few years back. They got the metric/imperial conversion wrong and the probe burnt up on entry.
No fear for overheating planes though. Modern alloys are up to the job.
Probably wouldn't handle the heat if they used Kelvin gauges though.
