Q:

Heat transfer through radiation and its relation with temperature

My question is: if a body and the surroundings have the exact same temperature, will that body still lose heat in terms of radiation? If so then what exactly is heat.
Heat is defined as energy flow between a system and another or between a system and its surroundings by virtue of the temperature difference. 
so no energy flow will occur if temperature difference between a body and its surroundings is zero. So no radiation should occur. But stefan-boltzmann implies that radiation energy is only dependent on absolute temperature of the body. Thus my confusion?
Another question: I learned that heat is transferred from a higher temperature body to a lower temperature body. Is this universal to all modes of heat transfer? If 2 bodies are seperated by a vacuum will the hot body lose heat through radiation and the cold body absorb that heat? So when both those bodies have the same temperature no radiation should occur as they are in thermal equilibrium? That being what is considered the temperature of vacuum that seperates the 2 bodies. Does it have temperature or is it undefined?

A:

I'll answer your second question first, because then your first one is easier. In short, yes, the equilibration of temperature between two bodies is absolutely universal - it doesn't depend on how the heat is transferred, and in particular it does apply to radiative transfer. And, indeed, once two bodies have reached thermal equilibrium through radiative transfer, the radiation in between them has a temperature that is the same as the temperature of the two bodies.
Let us now imagine two bodies coming into radiative equilibrium. We'll say that one of them is a hollow sphere and the other one is inside it, because then we don't have to consider the surrounding environment (which I'll get to shortly). The inner body will be giving off heat at a rate proportional to its temperature to the fourth power, and this doesn't depend on the temperature of its surroundings at all. But it's also absorbing heat, at a rate that does depend on the temperature of its surroundings. (It's proportional to the fourth power of the outer body's temperature.) So when they come into equilibrium, the inner body is giving off and receiving heat at exactly the same rate. Radiation is still occurring, but heat flow is not, because the radiation coming in cancels the radiation going out, so there's no net flow of energy. This answers your first question.
Often we don't consider this because we're thinking about something that's a lot hotter than its surroundings. Because $T^4$ increases very rapidly with $T$, the radiative energy transfer from the environment is often small enough to be ignored in this case. In particular, for a body in space that's not exposed to sunlight, the relevant incoming radiation is the cosmic microwave background, which has a temperature of only 3 kelvin and can be ignored for most purposes.

