Among the various sustainability goals of higher education institutions (HEIs), reducing energy use and carbon emissions are particularly important. However, not much is known about energy demand from the higher education - sector especially since there is a lack of robust models of energy demand in this sector. This paper, the first to utilize a panel dataset and advanced panel econometric techniques in order to model energy use in higher education, investigates variations in energy use between HEIs (cross-sectional analysis), and also changes in energy use over time (temporal analysis), using the UK as a case study. We argue that panel dataset and methods are more useful for understanding growth (and reduction) in energy use within the HE sector than the methods used within previous cross-sectional studies. Results show that, over time and also across the sector, energy consumption in the HEIs increases with increases in income and floor space, but at a slower rate. As HEIs grow overall (in terms of income, floor space, student and staff number) over time, they become more 'energy efficient' (using less energy per unit of area, population or income), indicating economies of scale in the temporal dimension. Results also show that after controlling for income and size, research intensive HEIs consume more energy. We also find a small but statistically significant effect of energy prices on energy consumption, as might be expected. Simulation using the model parameters for an example scenario suggests that energy consumption will continue to increase unless there is a significant change in the policies driving income growth and spatial expansion in the HE sector in the UK.