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In dffuse interstellar clouds the excitation temperature derived from the lowest levels of H$^+_3$ is systematically lower than that derived from H2. The differences may be attributed to the lack of state-specific formation and destruction rates of H$^+_3$ needed to thermalize the two species. Aims. In this work, we want to check the role of rotational excitation collisions of H$^+_3$ with atomic hydrogen on its excitation temperature. Methods. 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