Standard (black-box) regression models may not necessarily suffice for accurate identification and prediction of thermal dynamics in buildings. This is particularly apparent when either the flow rate or the inlet temperature of the thermal medium varies significantly with time. To this end, this paper analytically derives, using physical insight, and investigates linear regression models (LRMs) with nonlinear regressors (NRMs) for system identification and prediction of thermal dynamics in buildings. Comparison is performed with standard linear regression models with respect to both (a) identification error and (b) prediction performance within a model-predictive-control implementation for climate control in a residential building. The implementation is performed through the EnergyPlus building simulator and demonstrates that a careful consideration of the nonlinear effects may provide significant benefits with respect to the power consumption.