The thermal conductivity $kappa$ of superconductor Ir$_{1-x}$Pt$_{x}$Te$_2$ ($x$ = 0.05) single crystal with strong spin-orbital coupling was measured down to 50 mK. The residual linear term $kappa_0/T$ is negligible in zero magnetic field. In low magnetic field, $kappa_0/T$ shows a slow field dependence. These results demonstrate that the superconducting gap of Ir$_{1-x}$Pt$_{x}$Te$_2$ is nodeless, and the pairing symmetry is likely conventional s-wave, despite the existence of strong spin-orbital coupling and a quantum critical point.
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