A noise figure of 3dB, translates to an equivalent noise temperature equal to the room temperature. What is the significance of this relation? Is there a physical interpretation for this?
Noise figure (NF) is the decibel equivalent of noise factor (F) and noise factor is the amount an amplifier degrades the signal to noise ratio of a given input signal. The only significance this has with temperature is that the stated figure/factor of an amplifier will be at 290 kelvin (room temperature).
See this wiki page.
3dB is a doubling in noise power, implying two uncorrelated power sources of the same magnitude.
One source is inherent to the temperature of the sensor in its environment (not necessarily a room, it may be in space, or heated or cooled) and the other source is the excess noise of the system (eg amplifier) , which can also be modelled as having a temperature.
Why would you model it as a temperature? If you want to improve system performance by cooling either the amplifier or sensor, there's little to be gained by reducing the the noise temperature of one unit much below the other, and greater cooling becomes increasingly more expensive.
And it was an unexpected discrepancy in noise temperatures in radio astronomy, in a very low noise system with a high gain antenna, that led to the discovery of the 3K background radiation.