High resolution, ~50", measurements of the 170 micron and Hα luminosity have been compared at 36 locations within the spiral galaxy M51 in order to elucidate the origin of the far-infrared luminosity. After correcting the Hα luminosity for extinction and extrapolating the 170 micron luminosity to a 40-1000 micron far-infrared luminosity we find that the far-infrared luminosity is comparable to that expected from the O and B stars which are required to ionize the hydrogen gas. The results show that the far-infrared luminosity is in quantitative agreement with that expected from O and B stars at all locations within M51. Furthermore, IRAS HiRes 60 and 100 micron images of M51 indicate that the temperature of the dust responsible for the far-infrared luminosity is similar to that expected for dust in the vicinity of H II regions over the entire star forming disk of M51. The mass of dust required to radiate the 60 and 100 micron emission, measured for M51 by IRAS, is about a factor of 10 lower than the dust content of M5 1 estimated from the atomic and molecular gas masses and a Galactic gas/dust mass ratio. The most plausible explanation for the discrepancy is that the majority (~90%) of the dust within M51 is at wavelengths longward of 100 microns and must therefore be cooler than the ~33 K dust that dominates the emission measured by IRAS. The 170 micron measurement of M51, obtained by Smith [ApJ,261,463 (1982)], provides independent support for large quantities of cold dust as the 170 micron flux is significantly higher than would be expected if all the dust were radiating at the same temperature as that measured by IRAS. The high gas/warm dust mass ratio is used to constrain the mass of dust that radiates at wavelengths longward of 100 microns and the 60, 100, and 170 micron photometry is used to constrain the temperature of the dust. The constraints require the bulk, ~90%, of the dust mass within M51 to be cold with a temperature <= 16 K. Molecular gas dominates the interstellar medium within M51 and the temperature derived for the dust is consistent with that expected for dust in molecular clouds. The far-infrared luminosity of M51 is dominated by thermal emission from warm, ~33 K, dust even though most (~90%) of the dust mass within MS 1 is much colder with a temperature of 16 K. The ability for a small mass of warm dust to dominate the luminosity of significantly greater quantities of colder dust arises as a natural consequence of the strong temperature dependence of thermal emission.