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The extended shortwave infrared (eSWIR) band, spanning the wavelengths between 2 and 2.6 µm, lies between the traditional reflective and emissive bands. The eSWIR band receives fewer thermal photons from terrestrial targets than the midwave infrared (MWIR) or longwave infrared (LWIR) bands by several orders of magnitude, but thermal imaging in the band remains possible for a sufficiently hot target. This paper presents a theoretical rule for the minimum target temperature required to achieve a threshold contrast-to-noise ratio against a terrestrial background as a function of an eSWIR imaging system's <i>f</i>/<i>#</i>, pixel pitch, integration time, and throughput. Experimental data indicate the rule to be a robust predictor. Analysis of the rule provides limits on the tradespaces for system design, including requirements for focal plane array cooling, <i>f</i>/<i>#</i>, pixel pitch, and integration time. These limits indicate that typical thermal imaging tasks can be accomplished in nighttime conditions with unspecialized eSWIR systems. The potential advantages of eSWIR over the traditional thermal bands (MWIR and LWIR) are briefly discussed for two applications: urban reconnaissance and long-range aerial infrared search-and-track.