  The unknown temperature of a sample may be estimated with minimal disturbance
by putting it in thermal contact with an individual quantum probe. If the
interaction time is sufficiently long so that the probe thermalizes, the
temperature can be read out directly from its steady state. Here we prove that
the optimal quantum probe, acting as a thermometer with maximal thermal
sensitivity, is an effective two-level atom with a maximally degenerate excited
state. When the total interaction time is insufficient to produce full
thermalization, we optimize the estimation protocol by breaking it down into
sequential stages of probe preparation, thermal contact and measurement. We
observe that frequently interrogated probes initialized in the ground state
achieve the best performance. For both fully and partly thermalized
thermometers, the sensitivity grows significantly with the number of levels,
though optimization over their energy spectrum remains always crucial.
