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