  We investigate the resource theory for temperature estimation. We demonstrate
that it is the fluctuation of heat that fundamentally determines temperature
precision through the temperature-heat uncertainty relation. Specifically, we
find that heat is divided into trajectory heat and correlation heat, which are
associated with the heat exchange along thermometer's evolution path and the
correlation between the thermometer and the sample, respectively. Based on two
type of thermometers, we show that both of these heat terms are resources for
enhancing temperature precision. Additionally, we demonstrate that the
temperature-heat uncertainty relation is consistent with the well known
temperature-energy uncertainty relation in thermodynamics. By clearly
distinguishing the resources for enhancing estimation precision, our findings
not only explain why various quantum features are crucial for accurate
temperature sensing but also provide valuable insights for designing
ultrahigh-sensitive quantum thermometers.
