  We report resistivity $\rho$ and thermal conductivity $\kappa$ measurements
on Ca$_3$Ir$_4$Sn$_{13}$ single crystals, in which superconductivity with $T_c
\approx 7$ K was claimed to coexist with ferromagnetic spin-fluctuations. Among
three crystals, only one crystal shows a small hump in resistivity near 20 K,
which was previously attributed to the ferromagnetic spin-fluctuations. Other
two crystals show the $\rho \sim T^2$ Fermi-liquid behavior at low temperature.
For both single crystals with and without the resistivity anomaly, the residual
linear term $\kappa_0/T$ is negligible in zero magnetic field. In low fields,
$\kappa_0(H)/T$ shows a slow field dependence. These results demonstrate that
the superconducting gap of Ca$_3$Ir$_4$Sn$_{13}$ is nodeless, thus rule out
nodal gap caused by ferromagnetic spin-fluctuations.
