We have analyzed an XMM-Newton observation of the nearby spiral galaxy NGC 1313 , which contains two ‘ ‘ ultra-luminous ’ ’ X-ray ( ULX ) sources . We measure isotropic luminosities of L _ { X } = 2.0 \times 10 ^ { 40 } ~ { } erg~ { } s ^ { -1 } and L _ { X } = 6.6 \times 10 ^ { 39 } ~ { } erg~ { } s ^ { -1 } for NGC 1313 X-1 and X-2 ( 0.2-10.0 keV , assuming a distance of 3.7 Mpc ) . The spectra statistically require soft and hard spectral components to describe the continuum emission ; some prior studies of ULXs have claimed cool soft components with lower statistics . The improvement over several single-component models exceeds the 8 \sigma level of confidence for X-1 ; the improvement for X-2 is significant at the 3 \sigma level . The soft components in these ULX spectra are well-fit by multi-color disk blackbody models with color temperatures of kT \simeq 150 eV . This temperature differs markedly from those commonly measured in the spectra of stellar-mass ( 10 ~ { } M _ { \odot } ) black holes in their brightest states ( kT \simeq 1 keV ) . It is expected that the temperature of an accretion disk orbiting a black hole should decrease with increasing black hole mass . If the soft components we measure are due to emission from the inner region of an accretion disk , and disks extend close to the innermost stable circular orbit at the accretion rates being probed , the low color temperatures may be interpreted as spectroscopic evidence of black holes with intermediate masses : M _ { BH } \simeq 10 ^ { 3 } ~ { } M _ { \odot } . Simple Eddington scaling arguments suggest a mimum mass of M _ { BH } \sim 10 ^ { 2 } M _ { \odot } . NGC 1313 X-1 and X-2 are found in optical nebulae ( Pakull & Mirioni 2002 ) , which may indicate that anisotropic emission geometries are unlikely to account for the fluxes observed .