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Temperature and emissivity separation (TES) algorithms designed to work with mid-infrared (MIR) hyperspectral data are extremely limited. Two TES algorithms originally designed for long-wave infrared hyperspectral data, specifically, the iterative spectrally smooth (ISS) algorithm and the stepwise refining algorithm, are extended into MIR and renamed the extended iterative spectrally smooth (EISS) and extended stepwise refining algorithms (ESR), respectively. Numerical experiments are first conducted to evaluate their feasibility. The results of the numerical experiments indicate that the accuracy of the ESR algorithm is higher than that of the EISS algorithm. Moreover, the ESR algorithm is more robust than the EISS algorithm under sunlit conditions. Their accuracy is then validated with in situ measurements. Finally, the emissivity root mean square errors (RMSEs) of the EISS and ESR algorithms are compared with the data derived with the ISS algorithm using in situ measurements. Results show that the average emissivity RMSEs of 0.03 in 2000-2200 cm-1 and of 0.03-0.30 in 2400-3000 cm-1 for nighttime, and 0.02 in 2000-2200 cm-1 and 0.03 in 2500-3000 cm-1 for daytime, can be obtained from ground-based MIR hyperspectral data using the ESR algorithm.