In this paper, we formulate the energy-efficient cooperative sensing scheduling scheme for a cognitive radio network (CRN) with heterogeneous primary signal-to-noise ratio at each secondary user (SU). In the considered CRN, cognitive base station assigns a set of SUs for each frequency with the aim of minimizing the total energy consumption for sensing while meeting the asserted probability of detection and false alarm requirements by employing cooperation. Sensing duration for a target detection performance increases with degrading channel quality. Thus, an SU with better channel conditions consumes lower energy for sensing. Additionally, an SU also spends energy to switch to the next frequency in its sensing sequence. Our scheduling scheme discovers the appropriate set of SUs for each frequency by considering the sensing and channel switching energy as well as the energy consumed for reporting the sensing outcomes. We also present a polynomial time heuristic, Energy Aware Spectrum sEnsing (EASE) that performs close to the optimal solution.