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Phononic crystals (PnCs) emerge as an innovative sensor technology, especially for high-performance sensing applications. This study strives to advance this field by developing new designs of PnC structures that exhibit stability in the face of construction imperfections and deformations, focusing on the evolution of topological PnCs (TPnCs). These designs could be promising to overcome the problem of instability involved in most of the theoretical PnC sensors when they emerge in experimental verification. In particular, the fabrication process of any design could collide with some fluctuations in controlling the size of each component. Thus, Fano resonance is introduced through a one-dimensional (1D) quasiperiodic TPnC. To the best of the author’s knowledge, this study is the first to observe Fano modes in liquid cavities through 1D PnCs. Various quasiperiodic PnC designs are employed to detect the temperature of alcohols (specifically propanol) across an extensive temperature range (160–240 °C). The effects of many geometrical parameters on the sensor stability, such as material thicknesses, are studied. Numerical findings demonstrated that the designed quasiperiodic topological PnCs based on Fibonacci sequence of the second order proved superior performance. This sensing tool provides sensitivity, quality factor and figure-of-merit values of 104,533.33 Hz/°C, 223.69 and 0.5221 (/°C), respectively, through temperature detection of propanol in the range of 160–240 °C. [ABSTRACT FROM AUTHOR]