It is known that the Finsler heat flow is a nonlinear flow. This leads to the study of linearized heat semigroup for the Finsler heat flow. In this talk, we will introduce some properties of linearized heat semigroup and prove that the semigroup is conservative on complete Finsler measure spaces with weighted Ricci curvature bounded from below. As applications, we will give new proofs of Li-Yau's type inequalities for positive solutions to the heat flow established by Ohta-Sturm and myself respectively in compact case and generalize these inequalities to the complete noncompact case. Finally, we will give several equivalent characterizations of Ric_∞ ≥K(K∈ R) via the linearized heat semigroup approach.