In this paper, we present an investigation of the possibility to use a neural network combined with a quasi-physical description in order to predict the annual supplied space heating demand (P) for a number of small single family buildings located in the North of Sweden. As a quasi-physical description for P, we used measured diurnal performance data from a similar building or simulated data from a steady state energy simulation software. We show that the required supplied space heating demand may be predicted with an average accuracy of 5%. The predictions were based on access to measured diurnal data of indoor and outdoor temperatures and the supplied heating demand from a limited time period, ranging from 10 to 35 days. The prediction accuracy was found to be almost independent of what time of the year the measurements were obtained from, except for periods when the supplied heating demand was very small. For models based on measurements from May and for some buildings from April and September, the prediction was less accurate.