The paper introduces hidden grid background oriented schlieren for quantitative study and visualization of natural convection heat transfer. In this technique, the refractive index variation, induced by the temperature gradient, is encoded in the recorded signal phase through the distortion of a background pattern. The background (undistorted) pattern is implicit (or hidden) in the light source. Quantitative estimation of the phase map is obtained by windowed Fourier transform. This method offers localized processing of the signal using joint space-frequency representation. The performance of hidden grid background oriented schlieren is practically demonstrated by investigating natural convective flow, a demanding task due to its comparatively small heat transfer.