A systematic particle-in-cell investigation is reported focusing on the sheaths surrounding hot planar surfaces that are embedded in fusion plasmas with an arbitrary magnetic field inclination angle. The transition to the space-charge limited regime and the subsequent strict limitation of the escaping thermionic current density are demonstrated to be global characteristics of strongly emitting sheaths also in the presence of inclined magnetic fields. A physically transparent semi-empirical expression has been identified for the limited thermionic current as a function of the plasma conditions and inclination angle that is accurate for both the inter–and intra-ELM plasmas of present-day tokamaks.