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Time-resolved transmission spectroscopy of a mid-infrared quantum cascade laser emitting at 11.7 mum allows us to iteratively retrieve the effective refractive index and the extinction coefficient of the gain medium in a broad spectral range with an accuracy of +/-7x10(-3). Besides a 3% slowdown of the group velocity we find a large induced group-velocity dispersion with changing signs in the vicinity of the gain maximum, disclosing implications for self-pulse formation in quantum-cascade lasers. Additionally we measured the temperature in the active region by exploiting the thermo-optic effect. A linear behavior with respect to the current and the duty cycle was observed.