  The rapidly developing quantum technologies and thermodynamics have put
forward a requirement to precisely control and measure the temperature of
microscopic matter at the quantum level. Many quantum thermometry schemes have
been proposed. However, precisely measuring low temperature is still
challenging because the obtained sensing errors generally tend to diverge with
decreasing temperature. Using a continuous-variable system as a thermometer, we
propose non-Markovian quantum thermometry to measure the temperature of a
quantum reservoir. A mechanism to make the sensing error $\delta T$ scale with
the temperature $T$ as the Landau bound $\delta T\simeq T$ in the
full-temperature regime is discovered. Our analysis reveals that it is the
quantum criticality of the total thermometer-reservoir system that causes this
enhanced sensitivity. Efficiently avoiding the error-divergence problem, our
result gives an efficient way to precisely measure the low temperature of
quantum systems.
