A two-dimensional gradient-index phononic crystal (GRIN PnC) of steel cylinders in an ethanol matrix was designed and simulated for λ≥6a at room temperature. The hyperbolic secant profile of the refractive index is obtained by changing the scatterers radius of the structure in the transverse direction to gradually refract the waves. The finite element method is used to calculate the effective refractive index in each row of the structure and to investigate the propagation of acoustic waves in the gradual medium. With the help of gradient structure equations, the analytical beam trajectories were obtained and compared with the wave propagation results. The effect of temperature on the first band and thermal adjustment of the focal point for 0°C and 50°C have been investigated. The obtained results show that it is possible to shift the focal point at a certain frequency due to the changes of the effective refractive indices of the cylinders in the transverse positions for the calibration applications.