A controversy over the temperature distribution of coronal loops has arisen recently because different investigators using different techniques have obtained very different answers. Analysis of Solar and Heliospheric Observatory (SOHO) Extreme ultraviolet Imaging Telescope (EIT) and Transition Region and Coronal Explorer (TRACE) data using narrowband ratios to obtain temperature maps has produced several key publications that suggest that coronal loops may be isothermal. On the other hand, our analysis of the SOHO Coronal Diagnostics Spectrometer (CDS) spectral line data taken on 1998 April 20 for several pixels along a relatively isolated coronal loop on the southwest limb of the solar disk is clearly inconsistent with isothermal plasma along either the line of sight or the length of the loop. We have constructed a differential emission measure (DEM) distribution for each pixel; these distributions, taken together, suggested that the DEM-weighted temperature increases from the footpoints to the loop top. We convolved these DEM curves with the three different EIT coronal response functions. This gives us the intensity (in units of DN s-1) of what EIT would ``see'' in the 171, 195, and 284 Å passbands if it were observing the CDS loop. We take a ratio of these values (171 Å/195 Å and 195 Å/284 Å), and use the regular EIT software to calculate a temperature at each pixel for each ratio. EIT ``sees'' a loop with an almost uniform temperature, but the derived temperatures are different for the different ratios. These uniform-temperature loops arise even though the actual temperature input is multithermal both along the line of sight and along the length of the loop. We suspect that these apparent uniform-temperature loops may be an unfortunate by-product of the simplistic filter-ratio method that is used for both EIT and TRACE temperature analysis. Our results indicate that narrow-passband EUV observations must be used in conjunction with other diagnostics to draw quantitative conclusions about the properties of coronal plasma.