  A paradigm shift in quantum thermometry is proposed. To date, thermometry has
relied on local estimation, which is useful to reduce statistical fluctuations
once the temperature is very well known. In order to estimate temperatures in
cases where few measurement data or no substantial prior knowledge are
available, we build instead a theory of global quantum thermometry. Based on
scaling arguments, a mean logarithmic error is shown here to be the correct
figure of merit for thermometry. Its full minimisation provides an operational
and optimal rule to post-process measurements into a temperature reading, and
it establishes a global precision limit. We apply these results to the
simulated outcomes of measurements on a spin gas, finding that the local
approach can lead to biased temperature estimates in cases where the global
estimator converges to the true temperature. The global framework thus enables
a reliable approach to data analysis in thermometry experiments.
