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We address estimation of temperature for finite quantum systems at thermalequilibrium and show that the Landau bound to precision $\delta T^2 \proptoT^2$, originally derived for a classical {\em not too small} system being aportion of a large isolated system at thermal equilibrium, may be also achievedby energy measurement in microscopic {\em quantum} systems exhibiting vanishinggap as a function of some control parameter. On the contrary, for any quantumsystem with a non-vanishing gap $\Delta$, precision of any temperatureestimator diverges as $\delta T^2 \gtrsim T^4 e^{\Delta/T}$.

Achieving the Landau bound to precision of quantum thermometry in systems with vanishing gap