We study the thermally induced shape fluctuations of monodisperse emulsion droplets. The very small amplitude of these fluctuations is clearly resolved by diffusing wave spectroscopy and a theory is derived to describe the measured data. We measure the dependence of the fluctuations on droplet volume fraction φ, thereby directly probing the interplay between droplet interactions and droplet flexibility. The characteristic relaxation frequency of the fluctuations is found to decrease with increasing φ, while their amplitude increases.