Upon cooling, branched line defects develop in epitaxial graphene grown at high temperature on Pt(111) and Ir(111). Using atomically resolved scanning tunneling microscopy, we demonstrate that these defects are wrinkles in the graphene layer, i.e. stripes of partially delaminated graphene. With low energy electron microscopy (LEEM), we investigate the wrinkling phenomenon in situ. Upon temperature cycling, we observe hysteresis in the appearance and disappearance of the wrinkles. Simultaneously with wrinkle formation a change in bright field imaging intensity of adjacent areas and a shift in the moiré spot positions for micro diffraction of such areas takes place. The stress relieved by wrinkle formation results from the mismatch in thermal expansion coefficients of graphene and the substrate. A simple one-dimensional model taking into account the energies related to strain, delamination and bending of graphene is in qualitative agreement with our observations.