  The precision of typical thermometers consisting of $N$ particles is shot
noise limited, improving as $\sim1/\sqrt{N}$. For high precision thermometry
and thermometric standards this presents an important theoretical noise floor.
Here it is demonstrated that thermometry may be mapped onto the problem of
phase estimation, and using techniques from optimal phase estimation, it
follows that the scaling of the precision of a thermometer may in principle be
improved to $\sim1/N$, representing a Heisenberg limit to thermometry.
