The paper introduces a multi-scale processing method for quantitative study and visualization of convective heat transfer using diffractive optical element based background-oriented schlieren technique. The method relies on robust estimation of phase encoded in the fringe pattern using windowed Fourier transform and subsequent multi-scale characterization of the obtained phase using continuous wavelet transform. As the phase is directly mapped to the refractive index fluctuations caused by the temperature gradients, the multi-scale inspection provides interesting insights about the underlying heat flow phenomenon. The performance of the proposed method is demonstrated for quantitative flow visualization.