In this work a new model of the ion thermal transport, based on the long wavelength behaviour of the ion-temperature-gradient-driven turbulence, is introduced. A relevant property of the model is that the thermal conductivities grow with minor radius, as a consequence of the positive dependence of the correlation length and of the inverse of the correlation time on the ion temperature gradient. The model is assessed by comparing the predicted profiles of temperature and effective conductivity with the experimental profiles of several machines.