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We present a method for in situ temperature measurement of superconductingquantum circuits, by using the first three levels of a transmon device to whichwe apply a sequence of $\pi$ gates. Our approach employs projective dispersivereadout and utilizes the basic properties of the density matrix associated withthermal states. This method works with an averaging readout scheme and does notrequire a single-shot readout setup. We validate this protocol by performingthermometry in the range of 50 mK - 200 mK, corresponding to a range ofresidual populations $1\%-20 \%$ for the first excited state and $0.02\%-3 \%$for the second excited state.

Protocol for temperature sensing using a three-level transmon circuit