  This paper presents an alternative method to prove the heat kernel
asymptotics for the Kodaira Laplacian with respect to the high power of a
holomorphic Hermitian line bundle $(L,h^L)$ over a possibly non-compact
Hermitian manifold $(M,\omega)$. The approach used in this work employs a
scaling technique and is applicable to $M$ regardless of its compactness.
