Summary: In this paper, the low Mach number limit for the three-dimensional full compressible Navier-Stokes-Korteweg equations with general initial data is rigorously justified within the framework of local smooth solution. Under the assumption of large temperature variations, we first obtain the uniform-in-Mach-number estimates of the solutions in a \(\varepsilon \)-weighted Sobolev space, which establishes the local existence theorem of the three-dimensional full compressible Navier-Stokes-Korteweg equations on a finite time interval independent of Mach number. Then, the low mach limit is proved by combining the uniform estimates and a strong convergence theorem of the solution for the acoustic wave equations. This result improves that of K. Sha and Y. Li [Z. Angew. Math. Phys. 70, No. 6, Paper No. 169, 16 p. (2019; Zbl 1433.35295)] for well-prepared initial data.