Generalized Additive Models (GAM) are a widely popular class of regression models to forecast electricity demand, due to their high accuracy, flexibility and inter- pretability. However, the residuals of the fitted GAM are typically heteroscedastic and leptokurtic caused by the nature of energy data. In this paper we propose a novel approach to estimate the time-varying conditional vari-ance of the GAM residuals, which we call the GAM2 algorithm. It allows utility companies and network operators to assess the uncertainty of future electricity demand and incorporate it into their planning processes. The basic idea of our algorithm is to apply another GAM to the squared residuals to explain the dependence of uncertainty on exogenous variables. Empirical evidence shows that the residuals rescaled by the estimated conditional variance are approximately normal. We combine our modeling approach with online learning algorithms that adjust for dynamic changes in the distributions of demand. We illustrate our method by a case study on data from R6seau de transport d'electricite, the operator of the French transmission grid.