We observed a transequatorial loop (TEL) connecting NOAA Active Regions 10652 and 10653 at the west solar limb on 2004 July 29 with the Extreme-Ultraviolet Imaging Telescope (EIT) and the Coronal Diagnostic Spectrometer (CDS) aboard the Solar and Heliospheric Observatory. Only the loop's northern leg was observed with CDS. The loop appeared bright and cospatial in extreme-ultraviolet emission lines from ions formed over a wide range of temperature (T, in kelvins), including He I (logT=4.0), O III (logT=4.9), O IV (5.2), O V (5.4), Ne VI (5.6), Ca X (5.9), Mg X (6.1), and Fe XII (logT=6.1). This indicates that the loop plasma was multithermal and covered roughly 2 orders of magnitude in temperature. Our measurement of He I, O III, and O IV line emission reveals the coolest plasma ever detected in a TEL. The most likely explanation for the wide range of cospatial temperatures in the TEL is that it consisted of numerous sub-resolution strands, all at different temperatures. Each of the lines that are formed at temperatures less than 106 K exhibited relative Doppler blueshifts in the TEL that correspond to velocities toward the observer larger than 30 km s-1, where the two strongest cool lines (He I at 584.3 Å and O V at 629.7 Å) yielded maximum values of 37 and 41 km s-1, respectively. The presence of cool plasma in the TEL at heights several times those of the cool ions' scale heights suggests that the loop remained visible at low temperatures by maintaining a steady flow of cool plasma.