Previous analyses of ASCA data of clusters of galaxies have found conflicting results regarding the slope of the temperature profile of the hot X-ray gas within clusters, mainly because of the large, energy-dependent point-spread function (PSF) of the ASCA mirrors, We present a summary of all ASCA-determined cluster temperature profiles found in the literature and find a discrepancy in the radial temperature trend of clusters based on which PSF-correction routine is used, This uncertainty in the cluster temperature profile in turn can lead to large uncertainties in the amount of dark matter in clusters. In this study, we have used ROSAT PSPC data to obtain independent relative temperature profiles for 26 clusters, most of which have had their temperature profiles determined by ASCA. Our aim is not to measure the actual temperature values of the clusters but to use X-ray color profiles to search for a hardening or softening of the spectra as a function of radius for comparison to ASCA-derived profiles. The radial color profiles indicate that outside of the cooling flow region, the temperature profiles of clusters are in general constant. Within 35% of the virial radius, we find that a temperature drop of 20% at 10 keV and 12% at 5 keV can be ruled out at the 99% confidence level. A subsample of non-cooling flow clusters shows that the condition of isothermality applies at very small radii too, although cooling gas complicates this determination in the cooling how cluster subsample. The colors predicted from the temperature profiles of a series of hydrodynamical cluster simulations match the data very well, although they cannot be used to discriminate among different cosmologies. An additional result is that the color profiles show evidence for a central peak in metallicity in low-temperature clusters.