  Coulomb crystals of cold trapped ions are a leading platform for the
realisation of quantum processors and quantum simulations and, in quantum
metrology, for the construction of optical atomic clocks and for fundamental
tests of the Standard Model. For these applications, it is not only essential
to cool the ion crystal in all its degrees of freedom down to the quantum
ground state, but also to be able to determine its temperature with a high
accuracy. However, when a large ground-state cooled crystal is interrogated for
thermometry, complex many-body interactions take place, making it challenging
to accurately estimate the temperature with established techniques. In this
work we present a new thermometry method tailored for ion crystals. The method
is applicable to all normal modes of motion and does not suffer from a
computational bottleneck when applied to large ion crystals. We test the
temperature estimate with two experiments, namely with a 1D linear chain of 4
ions and a 2D crystal of 19 ions and verify the results, where possible, using
other methods. The results show that the new method is an accurate and
efficient tool for thermometry of ion crystals.
