It is not possible if there aren't valid temperature measurements available for all points throughout the measured period of time, so that many temperatures are "interpolated", estimated etc.
The measurements are real, and there is an established history of the models being generally correct (if not in specific details) by now. Climate study is not the new science you seem to think it is.
Can you point me to one such model? One that actually predicted temperatures correctly back in the 1970s and not after various recent "adaptations" like "corrected" emission data?
> The measurements are real
Yes, measurements are real. Interpolations, resulting "global" temperatures and predictions aren't.