Stellar density and bar strength should affect the temperatures of the cool (T ~ 20-30 K) dust component in the inner regions of galaxies, which implies that the ratio of temperatures in the circumnuclear regions to the disk should depend on Hubble type. We investigate the differences between cool dust temperatures in the central 3 kpc and disk of 13 nearby galaxies by fitting models to measurements between 70 and 500 microns. We attempt to quantify temperature trends in nearby disk galaxies, with archival data from Spitzer/MIPS and new observations with Herschel/SPIRE, which were acquired during the first phases of the Herschel observations for the KINGFISH (key insights in nearby galaxies: a far-infrared survey with Herschel) sample. We fit single-temperature modified blackbodies to far-infrared and submillimeter measurements of the central and disk regions of galaxies to determine the temperature of the component(s) emitting at those wavelengths. We present the ratio of central-region-to-disk-temperatures of the cool dust component of 13 nearby galaxies as a function of morphological type. We find a significant temperature gradient in the cool dust component in all galaxies, with a mean center-to-disk temperature ratio of 1.15 +/- 0.03. The cool dust temperatures in the central ~3 kpc of nearby galaxies are 23(+/-3)% hotter for morphological types earlier than Sc, and only 9(+/-3)% hotter for later types. The temperature ratio is also correlated with bar strength, with only strongly barred galaxies having a ratio over 1.2. The strong radiation field in the high stellar density of a galactic bulge tends to heat the cool dust component to higher temperatures, at least in early-type spirals with relatively large bulges, especially when paired with a strong bar.