From the statistical study of 162 profiles of meteorological balloons equipped with microthermal sensors, a new model is proposed, linking the temperature fluctuation structure constant (C2T) to the gradient of the mean potential temperature. This model is able to provide a vertical profile of the optical turbulence index (C2N) from a temperature profile, with a 1 km vertical resolution. Compared with the Vernin-Tatarski model and the median C2N profile, it gives better results as a profiler and seeing estimator. Within a large seeing distribution between 0.3" and 3", 58% are estimated with less than 30% of error. Our model fits well this wide median seeing range, which extends from 0.7" at Cerro Pachón to 2.9" at the South Pole.