Conventional criticality-based quantum metrological schemes work only at zero or very low temperature because the quantum uncertainty around the quantum phase-transition point is generally erased by thermal fluctuations with the increase of temperature. Such an ultralow-temperature requirement severely restricts the development of quantum critical metrology. In this paper, we propose a thermodynamic-criticality-enhanced quantum sensing scenario at finite temperature. In our scheme, a qubit is employed as a quantum sensor to estimate parameters of interest in the Dicke model which experiences a thermodynamic phase transition. It is revealed that the thermodynamic criticality of the Dicke model can significantly improve the sensing precision. Enriching the scope of quantum critical metrology, our finding provides a possibility to realize highly sensitive quantum sensing without cooling.