The power rating of Modular Multilevel Converter based HVDC has increased rapidly over the past decade, with individual links in the gigawatt power range now technically feasible and further power increases on the horizon. Such large links may be required to provide ancillary services such as fast frequency response or emergency power re-routing in the event of a system disturbance. Providing such services may require converters to be designed with overload capacity. This paper examines how the thermal aspects of semiconductor devices may impact the operation of such converters and how the exploitation of short-term thermal dynamics may lead to dynamic overload rating.