A new concept in the power system management is the asynchronous connection of grids. This connection occurs at different voltage and power level: high voltage, with HVDC systems, and medium/low voltage, with back-to-back converters and Smart Transformers. The decoupling of the power flow between the two grids allows higher controllability, including the possibility to control grid voltage and frequency independently in the two grids. This work aims to investigate and mitigate the thermal stress in grid-forming converters (e.g., Smart Transformers) applying a load voltage-sensitivity control. Depending on the nature of the loads, their power consumption varies with the voltage. This response is dependent on the connected loads and can be characterized by constant power (independent from the voltage), constant current (linearly dependent on the voltage) and constant impedance behavior (squared-dependent on the voltage). The sensitivity to voltage is exploited to control the load power consumption, reducing the junction temperature fluctuations and thus the power semiconductors stress. As a consequence, the converter operational range can be increased, reducing at the same time the stress for the power semiconductors.