We analyze thermal emission spectra using the 2001 Mars Odyssey Thermal Emission Imaging System (THEMIS) and the Mars Global Surveyor (MGS) Thermal Emission Spectrometer (TES) to characterize grain size and mineralogical composition of dunes at Hargraves crater, Mars. Thermal inertia and bulk composition of the dunes were compared to inferred provenances from the thermal infrared response of surface constituent materials. We use a Markov Chain Monte Carlo (MCMC) technique to estimate the bulk amount of mineralogy contributed by each inferred provenance to the dune field composition. An average thermal inertia value of 238+/-17 Jm-2K-1s-0.5 was found for the dunes corresponding to a surface composed of an average effective grain size of ~391+/-172 um. This effective particle size suggests the presence of mostly medium sand-sized materials mixed with fine and coarse grain sands. The dunes are likely comprised of a weakly indurated surface mixed with unconsolidated materials. Compositional analysis specifies that the dunes are comprised of a mixture of feldspar, olivine, pyroxene, and relatively low bulk-silica content. Dune materials were likely derived from physical weathering, especially eolian erosion, predominantly from the crater ejecta unit at the crater, mixed with a small amount from the crater floor and crater rim and wall lithologies - indicating the dune materials were likely sourced locally.