Final answer:
B) Temperature control thermostat. The temperature control thermostat is responsible for monitoring cabinet temperature in a frost-freezer and deactivating the heating coil when it exceeds the set limit.
Step-by-step explanation:
The component in a frost-freezer that monitors cabinet temperature and deactivates the heating coil when it rises above the set limit is the Temperature control thermostat (B). The temperature control thermostat senses the temperature inside the cabinet and sends a signal to the heating coil to turn off when the temperature exceeds the set limit. This helps maintain the desired temperature and prevents the freezer from constantly running and consuming excessive energy.