  The in-plane resistivity $\rho$ and thermal conductivity $\kappa$ of
FeAs-based superconductor KFe$_2$As$_2$ single crystal were measured down to 50
mK. We observe non-Fermi-liquid behavior $\rho(T) \sim T^{1.5}$ at $H_{c_2}$ =
5 T, and the development of a Fermi liquid state with $\rho(T) \sim T^2$ when
further increasing field. This suggests a field-induced quantum critical point,
occurring at the superconducting upper critical field $H_{c_2}$. In zero field
there is a large residual linear term $\kappa_0/T$, and the field dependence of
$\kappa_0/T$ mimics that in d-wave cuprate superconductors. This indicates that
the superconducting gaps in KFe$_2$As$_2$ have nodes, likely d-wave symmetry.
Such a nodal superconductivity is attributed to the antiferromagnetic spin
fluctuations near the quantum critical point.
