We report multi-wavelength power spectra of diffuse Galactic dust emission from BLAST observations at 250 , 350 , and 500 µm in Galactic Plane fields in Cygnus X and Aquila . These submillimeter power spectra statistically quantify the self-similar structure observable over a broad range of scales and can be used to assess the cirrus noise which limits the detection of faint point sources . The advent of submillimeter surveys with the Herschel Space Observatory makes the wavelength dependence a matter of interest . We show that the observed relative amplitudes of the power spectra can be related through a spectral energy distribution ( SED ) . Fitting a simple modified black body to this SED , we find the dust temperature in Cygnus X to be 19.9 \pm 1.3  K and in the Aquila region 16.9 \pm 0.7  K. Our empirical estimates provide important new insight into the substantial cirrus noise that will be encountered in forthcoming observations .