In future power systems, reduced overall inertia caused by an increased dominance of asynchronous generation and interconnections would make frequency control particularly challenging. As the number and power rating of voltage source converter (VSC) HVDC systems increases, network service provision would be expected from such systems and to do so would require overload capacity to be included in the converter specifications. This paper studies the provision of frequency services from modular multilevel converter (MMC)-based VSC HVDC interconnections using temperature-constrained overload capability. Overload of the MMC-based HVDC system is achieved through controlled circulating currents, at the expense of higher losses, and subject to a control scheme that dynamically limits the overload available in order to keep the semiconductor junction temperatures within operational limits. Two frequency control schemes that use the obtained overload capacity to provide frequency response during emergency conditions are investigated. The controllers' performance is demonstrated in the context of the future Great Britain transmission grid through a reduced equivalent test system. Simulation results show that even modest temperature margins which allow overload of MMC-based HVDC systems for a few seconds are effective as a primary frequency reserve and also reduce the loss of infeed requirements of such interconnections.