We present new constraints on the high-temperature emission measure of a non-flaring solar active region using observations from the recently flown Focusing Optics X-ray Solar Imager sounding rocket payload. FOXSI has performed the first focused hard X-ray (HXR) observation of the Sun in its first successful flight on 2012 November 2. Focusing optics, combined with small strip detectors, enable high-sensitivity observations with respect to previous indirect imagers. This capability, along with the sensitivity of the HXR regime to high-temperature emission, offers the potential to better characterize high-temperature plasma in the corona as predicted by nanoflare heating models. We present a joint analysis of the differential emission measure (DEM) of active region 11602 using coordinated observations by FOXSI, Hinode/XRT and Hinode/EIS. The Hinode-derived DEM predicts significant emission measure between 1 MK and 3 MK, with a peak in the DEM predicted at 2.0-2.5 MK. The combined XRT and EIS DEM also shows emission from a smaller population of plasma above 8 MK. This is contradicted by FOXSI observations that significantly constrain emission above 8 MK. This suggests that the Hinode DEM analysis has larger uncertainties at higher temperatures and that >8 MK plasma above an emission measure of 3x10^44 cm^-3 is excluded in this active region.