  We derive an interpolation version of constrained matrix Li-Yau-Hamilton
estimate on K\"ahler manifolds. As a result, we first get a constrained matrix
Li-Yau-Hamilton estimate for heat equation on a K\"ahler manifold with fixed
K\"ahler metric. Secondly, we get a corresponding estimate for forward
conjugate heat equation on K\"ahler manifolds with time dependent K\"ahler
metrics evolving by K\"ahler-Ricci flow.
