There is significant recent interest in applying model-based control techniques to improve the energy efficiency of buildings. This requires a predictive model of the building's thermal dynamics. Due to the complexity of the underlying physical processes, usually system identification techniques are used to identify parameters of a physics-based model. We investigate the effect of various model structures and identification techniques on the parameter estimates through a combination of analysis and experiments conducted in a commercial building. We observe that a second order model can reproduce the input-output behavior of a full-scale model (with 13 states). Even a single state model has enough predictive ability that it may be sufficient for control purposes. We also show that the application of conventional techniques to closed-loop data from buildings (that are collected during usual operation) leads to poor estimates; their inaccuracy becomes apparent only when forced-response data is used for validation where there is sufficient difference among various inputs and outputs. The results of this investigation are expected to provide guidelines on do's and don'ts in modeling and identification of buildings for control.