© 2018 Elsevier B.V. A significant portion of all energy generated is used to heat and cool buildings. Some of that energy can be saved by using a temperature controller with access to an accurate forecast of a building's internal temperature. These forecasts depend on information gathered from sensors, including temperature, humidity, sunlight, and the electrical load of cooking and laundry appliances. Using publicly available data from two homes with a wide variety of sensors, we forecast internal temperature by modelling it as a linear function of recent sensor values. These models are built using techniques that improve upon standard least squares regression: forward stepwise, ridge and lasso regressions, using cross-validation. With lasso regression, we accurately forecast internal temperature every quarter hour over the next 48 h within 1.8°C in both houses. We also forecast temperature changes over each quarter-hour for the next two days, within 0.05°C, which significantly improves on previous forecasts of temperature changes using the same data. We propose a business model for forecasting as a service, where guarantees of consistent accuracy are important for attracting clients and saving energy.