The hedging of weather risks has become extremely relevant in recent years, promoting the diffusion of weather-derivative contracts. The pricing of such contracts requires the development of appropriate models for the prediction of the underlying weather variables. Within this framework, a commonly used specification is the ARFIMA-GARCH. We provide a generalization of such a model, introducing time-varying memory coefficients. Our model satisfies the empirical evidence of the changing memory level observed in average temperature series, and provides useful improvements in the forecasting, simulation, and pricing issues related to weather derivatives. We present an application related to the forecast and simulation of a temperature index density, which is then used for the pricing of weather options. Copyright © 2011 John Wiley & Sons, Ltd.