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 ± 1.3 K and in the Aquila region 16.9 ± 0.7 K. Our empirical estimates provide important new insight into the substantial cirrus noise that will be encountered in forthcoming observations.