Final answer:
The device in question that senses outlet temperature and adjusts for varying hot or cold water temperature is a thermostatic mixing valve.
Step-by-step explanation:
A mixing valve that senses outlet temperature and compensates for fluctuations in incoming hot or cold water temperature is known as a thermostatic mixing valve. This valve is designed to maintain a consistent output water temperature, preventing scalding or thermal shock due to sudden temperature changes. It is a type of thermostat specifically designed for mixing water at predetermined temperatures.