  The in-plane resistivity $\rho$ and thermal conductivity $\kappa$ of
extremely overdoped KFe$_2$As$_2$ ($T_c$ = 3.0 K) single crystal were studied.
It is found that $\rho \sim T^{1.5}$ at low temperature, a typical non-Fermi
liquid behavior of electrons scattered by antiferromagnetic spin fluctuations.
In zero field, we observed a large residual linear term $\kappa_0/T$, about one
third of the normal-state value. In low magnetic fields, $\kappa_0/T(H)$
increases very fast. Such a behavior of $\kappa_0/T$ mimics the d-wave cuprate
superconductors, therefore provides clear evidence for nodes in the
superconducting gap of KFe$_2$As$_2$. Based on the Fermi surface topology of
KFe$_2$As$_2$, it is believed that the dominant intraband pairing via
antiferromagnetic spin fluctuations results in the unconventional
superconducting gap with nodes.
