Controllable building loads have the potential to increase the flexibility of power systems. A key step in developing effective and attainable load control policies is modeling the set of feasible building load profiles. In this paper, we consider buildings whose source of flexibility is their HVAC loads. We propose a data-driven method to empirically estimate a robust feasible region of the load using coarse data, that is, using only total building load and average indoor temperatures. The proposed method uses easy-to-gather coarse data and can be adapted to buildings of any type. The resulting feasible region model is robust to temperature prediction errors and is described by linear constraints. The mathematical simplicity of these constraints makes the proposed model adaptable to many power system applications, for example, economic dispatch, and optimal power flow. We validate our model using data from EnergyPlus and demonstrate its usefulness through a case study in which flexible building loads are used to balance errors of wind power forecasts.