The concept of the temperature of empty space, even in the absence of any matter or radiation, is a fascinating and complex topic in physics. According to our current understanding, even after the hypothetical scenario of the Heat Death of the universe, the temperature of empty space, often referred to as the "cosmic microwave background radiation," would not be precisely zero Kelvin.
The cosmic microwave background radiation (CMB) is the remnant radiation from the early stages of the universe, which has been stretched and cooled down due to the expansion of space. It is observed as a faint, nearly uniform background radiation with a temperature of about 2.7 Kelvin above absolute zero. This temperature represents the average temperature of space on a cosmological scale.
In the context of the Heat Death scenario, where the universe has reached a state of maximum entropy and all energy has been uniformly dispersed, the CMB would still persist. However, it is important to note that the CMB itself is not a direct measure of the temperature of empty space but rather a remnant from the Big Bang.
In the framework of our current understanding, even though the CMB temperature would persist, the energy density of the universe would become extremely dilute as it expands and approaches maximum entropy. As a result, the temperature ascribed to empty space, or the average energy per unit volume, would become vanishingly small but not exactly zero. However, it is essential to recognize that the topic of temperature in the context of the Heat Death of the universe and the behavior of space at extremely low energy states is still an active area of research, and future discoveries might provide further insights.