  Measuring the temperature of a quantum system is an essential task in almost
all aspects of quantum technologies. Theoretically, an optimal strategy for
thermometry requires measuring energy which demands full accessibility over the
entire system as well as complex entangled measurement basis. In this paper, we
take a different approach and show that single qubit sequential measurements in
the computational basis not only allows precise thermometry of a many-body
system but may also achieve precision beyond the theoretical bound, avoiding
demanding energy measurements at equilibrium. To obtain such precision, the
time between the two subsequent measurements should be smaller than the
thermalization time so that the probe never thermalizes. Therefore, the
non-equilibrium dynamics of the system continuously imprint information about
temperature in the state of the probe. This allows the sequential measurement
scheme to reach precision beyond the accuracy achievable by complex energy
measurements on equilibrium probes.
