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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., Comment: 5 pages, 4 figures