  We obtain two-sided estimates for the heat kernel (or the fundamental
function) associated with the following fractional Schr\"odinger operator with
negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on
$\RR^d$, where $\alpha\in(0,d\wedge 2)$ and $\lambda>0$. The proof is purely
analytical but elementary. In particular, for upper bounds of heat kernel we
use the Chapman-Kolmogorov equation and adopt self-improving argument.
