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We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough $P/E_y$ (pressure/Young's modulus) and $P/\rho v^2$ (P/kinetic energy density) elastic dominates kinetic energy, and energy fluctuations become primarily elastic in nature. This regime has likely been reached in recent experiments. We consider a generalization of the granular temperature, $T_{\ab{g}}$, with both kinetic and elastic terms and that changes smoothly from one regime to the other. This $T_{\ab{g}}$ is roughly consistent with a temperature adapted from equilibrium statistical mechanics.