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InI single crystals are a promising room temperature detector material for X-rays and γ-rays. To improve crystal growth of the material by simulations, knowledge of thermophysical properties is essential, and since InI is orthorhombic, the anisotropy has to be taken into account. The temperature dependence of several thermophysical properties have been measured for InI, including the anisotropic thermal expansion, specific heat, and the thermal diffusivity in the b direction. The anisotropic thermal expansion coefficients, determined by X-ray diffraction, were α11=1.03·10-5 K-1, α22= 3.77·10-5 K-1, and α33 = 6.26·10-5 K-1. The specific heat, measured by DSC, was 0.226 J g-1 K-1 at 335K, with a temperature dependence of 9.582·10-5 J g-1 K-2. In the course of the X-ray diffraction and DSC measurements, it was shown that supposed phase changes, reported in older literature, are actually not phase changes but oxidation effects. The thermal diffusivity in the b direction, measured by the Xenon Flash method, was 0.288·10-6 m2s-1 at RT, decreasing to 0.253·10-6 m2 s-1 at 450K. In addition, the volume increase upon melting and the thermal expansion of the melt have been determined.