  Improving the measurement precision of low temperature is significant in
fundamental science and advanced quantum technology application. However, the
measurement precision of temperature $T$ usually diverges as $T$ tends to 0.
Here, by utilizing a heavy impurity to measure the temperature of a Bose gas,
we obtain the Landau bound to precision $\delta^2 T\propto T^2$ to avoid the
divergence. Moreover, when the initial momentum of the heavy impurity is fixed
and non-zero, the measurement precision can be $\delta^2 T\propto T^3$ to break
the Landau bound. We derive the momentum distribution of the heavy impurity at
any moment and obtain the optimal measurement precision of the temperature by
calculating the Fisher information. As a result, we find that enhancing the
expectation value of the initial momentum can help to improve the measurement
precision. In addition, the momentum measurement is the optimal measurement of
the temperature in the case of that the initial momentum is fixed and not equal
to 0. The kinetic energy measurement is the optimal measurement in the case of
that the expectation value of the initial momentum is 0. Finally, we obtain
that the temperatures of two Bose gases can be measured simultaneously. The
simultaneous measurement precision is proportional to $T^2$ when two
temperatures are close to $T$.
