We have studied by atomic force microscopy (AFM, topographical imaging) the evolution of a single PEER spherulite in a thin film during isothermal cold-crystallization and upon subsequent reheating to increasingly higher temperatures. To open the spherulitic microstructure, we added 30% w/w of an amorphous diluent (poly(ether-imide), PEI) serving as a marker. Small-angle X-ray scattering and dynamic mechanical analysis mere used to check on bulk samples that similar structural evolutions are obtained when reheating cold-crystallized PEEK and a 70/30 PEEK/PEI blend. We then monitored at T-c = 180 degrees C the isothermal growth of a single PEEK spherulite in a thin film of the PEEK/PEI blend and followed the growth and branching of individual PEEK fibrils, separated by channels of rejected PEI. Further, we examined the changes in semicrystalline morphology induced by subsequent reheating. The spatial locations of the fibrils (i.e., lamellar stacks) of this very spherulite were not modified up to an annealing temperature of about 300 degrees C. However, the surface of the fibrils became covered with numerous small protuberances (diameter : 50-200 nm) growing in size and in number as annealing temperature increased. We consider these images to be the first direct-space proof for the existence of a large-scale melting-recrystallization process occurring when reheating cold-crystallized PEEK.