Acoustic temperature measurement of boilers relies heavily on the estimation accuracy and real-time performance of acoustic propagation time delay. To address the limitation of traditional methods, which can only estimate the delay with integer times of the sampling points, this paper proposes a high-precision multiplexed delay estimation method based on phase compensation. This method constructs a sinusoidal-chirp composite signal, and realizes high-precision delay estimation by combining generalized cross-correlation and phase estimation with the all-phase Fourier transform. Through simulation and experimental verification, the accuracy of the signal constructed in this paper matches that of other commonly used signals when using the generalized quadratic inter-correlation method. With phase compensation, it has higher accuracy and noise immunity, improving precision by more than 8. 5 times, and showing minimal impact form sampling frequency. This method maintains consistent performance in multi-channel synchronous time delay estimation using frequency division multiplexing, reducing the measurement time to 1 / 8 of traditional methods. It provides an effective solution to achieve faster and more accurate acoustic temperature measurements.