The morphology of poly(styrene-b-ethylene-r-butylene) (SEB) and poly(styrene-b-ethylene-r-butylene-b-styrene) (SEBS) thin films annealed both above (165 degrees C) and below (125 degrees C) the bulk order order transition temperatures (OOT) (similar to 140 degrees C) was characterized with grazing incidence small-angle X-ray scattering (GISAXS), dynamic secondary ion mass spectrometry (d-SIMS), and atomic force microscopy (AFM). The SEBS thin film morphology is always spherical, regardless of film thickness or annealing temperature, leading us to conclude that the OOT for films up to five layers of spheres is depressed by at least 10 degrees C relative to the bulk. In contrast, the SEB film morphology at both 125 and 165 degrees C is always cylindrical, except when the film thickness is less than t(cyl), a monolayer of cylinders. For SEB film thicknesses, t, less than t(cyl) at 165 degrees C either a partial or full monolayer of spheres forms (thickness t(sph)) with coexistence of patches of spheres and cylinders when t(sph) < t < t(cyl). Thus, we conclude that the OOT for SEB film thickness between t(cyl) and 5t(cyl) is increased by at least 20 degrees C over that of the bulk. This complex phase behavior can be understood qualitatively by considering two small contributions to the free energy f per block copolymer chain in the films: (1) an increase in f due to packing frustration and (2) a decrease in f due to the entropy of chain ends near the block copolymer film surfaces. The SEBS has no chain ends near the surface, and we propose that the larger packing frustration of SEBS chains in the square Wigner-Seitz cells of the cylinder monolayer, and the surface half-layers in thicker films, leads to the stabilization of the spherical morphology, which has a smaller packing frustration in the monolayer and surface half-layers. The SEB cylinders and sphere monolayers have the same packing frustration as those of the SEBS, but the contribution of the added entropy of chain ends near the surface is larger for the cylinders than for the spheres, more than offsetting the effect of packing frustration and thus stabilizing the cylindrical morphology at temperatures above the OOT.