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.