Weather constitutes an important macroeconomic risk that affects a wide range of industries, among them agriculture, energy and tourism. Companies in these sectors are naturally concerned about unfavorable weather conditions and much attention is paid to the development of risk management tools that deal with weather perils. We present a time series approach for modeling temperature dynamics, which is of special relevance for the pricing of weather/energy derivatives and weather insurance products. A seasonal mean least absolute shrinkage and selection operator-type technique based on a multiplicative structure of Fourier and generalized autoregressive conditional heteroscedasticity (GARCH) terms in volatility is proposed. The model describes the stylized facts of temperature: seasonality, intertemporal correlations and the heteroscedastic behavior of residuals. The application to European temperature data indicates that the multiplicative model for seasonal variance performs better in terms of out-of-sample forecast than other models proposed in the literature for modeling temperature dynamics.