Despite the decade-long study of the effect of nanoconfinement on the glass-transition temperature (T(g)) of amorphous materials, the quest to probe the distribution of T(g)s in nanoconfined glass formers has remained unfulfilled. Here the distribution of T(g)s across polystyrene films has been obtained by a fluorescence/multilayer method, revealing that the enhancement of dynamics at a surface affects T(g) several tens of nanometres into the film. The extent to which dynamics smoothly transition from enhanced to bulk states depends strongly on nanoconfinement. When polymer films are sufficiently thin that a reduction in thickness leads to a reduction in overall T(g), the surface-layer T(g) actually increases with a reduction in overall thickness, whereas the substrate-layer T(g) decreases. These results indicate that the gradient in T(g) dynamics is not abrupt, and that the size of a cooperatively rearranging region is much smaller than the distance over which interfacial effects propagate.