The rotationally resolved infrared spectra of single SF6 molecules embedded in large He-3 droplets have been studied as a function of mean sizes between (N) over bar(3) = 2 X 10(3) and 10(5) atoms by the cluster beam depletion technique. The observed frequency shifts and line broadening of the dopant spectra are interpreted in terms of the small impurity of about 30-50 He-4 atoms, which because of their lower zero point energy completely surround the SF6 molecule. For the largest droplets, the observed rotational structure is similar to that observed in pure He-4 droplets but the rotational temperature as determined from the relative line intensities is T-rot = 0.15(1) K, which is about a factor 2.5 lower than in pure He-4 droplets. The lower temperature is expected on the basis of the lower heat of evaporation of the He-3 atoms on the outside of the droplet. Mixed He-3/He-4 droplets produced by increasing the He-4 concentration in the source gas to 1.2 and 4% of the He-3 were found to have temperatures between that for the almost pure He-3 droplets and that for pure He-4 droplets.