We report a theoretical investigation of thermal hysteresis of fourfold anisotropy ferromagnetic ͑FM͒ film exchange coupled to a compensated antiferromagnetic substrate. Thermal hysteresis occurs if the temperature interval includes the reorientation transition temperature, below which the frustration of the interface exchange coupling leads to a 90°rotation of the magnetization of the ferromagnetic layer. The temperature width of the thermal hysteresis is tunable by external magnetic fields of modest magnitude, with values of 43 K for an external field of 110 Oe and of 14 K for a field of 210 Oe, for a Fe͑12 nm͒ / MnF 2 ͑110͒ bilayer. For a Fe͑3 nm͒ / FeF 2 ͑110͒ bilayer the width of the thermal hysteresis is 23 K at 110 Oe and 13 K at 300 Oe. We discuss how the thickness of the iron film affects the field tuning of the thermal hysteresis width, and also how the thermal loops may be used to identify the nature of the interface exchange energy.