A novel model of the electrical demand of a power system capable of representing hourly power and its dependence on temperature is presented. The application of the model to the Colombian system is shown with an evaluation of the error obtained. For the simulation of the optimal operation of systems with a high participation of renewable energies, a model such as the one presented is of vital importance in order to take into account the dependence of demand on meteorological variables. It is also necessary for the simulation of the expected effects of climate change on electricity demand.