Recent experiments have shown surprisingly large thermal time constants in suspended graphene ranging from 10 to 100 ns in drums with a diameter ranging from 2 to 7 μm. The large time constants and their scaling with diameter points toward a thermal resistance at the edge of the drum. However, an explanation of the microscopic origin of this resistance is lacking. Here, we show how phonon scattering at a kink in the graphene, e.g., formed by sidewall adhesion at the edge of the suspended membrane, can cause a large thermal time constant. This kink strongly limits the fraction of flexural phonons that cross the suspended graphene edge, which causes a thermal resistance at its boundary. Our model predicts thermal time constants that are of the same order of magnitude as experimental data and shows a similar dependence on the circumference. Furthermore, the model predicts the relative in-plane and out-of-plane phonon contributions to graphene's thermal expansion force, in agreement with experiments. We thus show an unconventional thermal boundary resistance which occurs solely due to strong deformations within a two-dimensional material.