Does placing a cold bottle next to an incubator cool the incubator through convection or radiation? Context for question: My girlfriend who is studying to be a nurse asked me to explain the difference between radiation and convection in context of the above question.
My answer: Radiation is the emission of heat by all bodies as long as their temperature is above 0K. Which means that convection would be how the baby would be affected and not by radiation.
The problem: It seems there are several nursing books (such as this one ) and even a physics book that seems to agree that apparently there is "cold" radiation as well.
I don't get it, can you radiate "cold"? If someone can explain how a cold wall/cold bottle/ cold anything would affect the baby by radiation (and not by convection).
 A: There is no such thing as cold radiation.
In the examples you link above, the issue is that the walls of the incubator are colder than the air or the baby.  What actually happens in this situation is this: all objects radiate with a certain intensity which is based on their temperature (among other things).  A baby in an incubator is constantly radiating energy away into the surrounding air and parts of the incubator; what keeps the baby warm is the fact that this same air and incubator radiate the same amount of heat back to the baby as the baby is losing.  As long as this balance is maintained the baby can maintain its body temperature.
In the case of the cold incubator wall, the situation is not that the incubator wall radiates cold to the baby but that the baby continues to radiate energy away (which it would be doing no matter where in the incubator it was at) but because the wall of the incubator is cold (in some relative sense) the amount of energy being radiated by the incubator wall back on to the baby is lower than would be if the wall was warm.  Because of this, the baby radiates away more energy than it is receiving from its surroundings (because the wall isn't radiating as much because of its lower temperature).  Thus the baby cools down.
A: @Joshua's answer is correct and addresses "cold wall of incubator". I want to add on the more general question

I don't get it, can you radiate "cold"? If someone can explain how a cold wall/cold bottle/ cold anything would affect the baby by radiation (and not by convection).

Everything reaches a radiation balance given time, the radiation leaving a body  and the radiation impinging from the surroundings ( including air) reach a balance and the temperatures equalize, environment and body.
When there is generation of heat in a body, as with a baby, the temperature is higher and is sustained higher than the environment. A baby in a crib with enough covers adjusts its temperature easily through biological mechanisms. A premature baby has not yet well developed all these mechanisms of response to environment. An incubator creates an environment to buffer the changes happening in a crib in an open air, and keeps the loss of energy from the baby at a comfortable and safe range.
Convection in liquids and air happens when there are differences in temperature within the mass. Convection transfers mass at a given temperature,  and thus the black body radiation balance between the room and the incubator can change, the incubator radiating from the walls more energy than it would if the air were warmer. This is the way cooling by fans work , in a computer for example. A fan brings in cooler air for the radiation balance and takes away the heated air that would keep the temperature of the mother board higher . 
Thus convection works with changes in the boundary conditions in the given situation, changing the temperature of the environment in which the body is embedded. Within an incubator though, there is not enough mass of air to create convective currents of any strength unless the temperature difference baby/wall is enormous, and even then it is the radiative loss that is dominant.

Does placing a cold bottle next to an incubator cool the incubator through convection or radiation?

A cold bottle next to an incubator will also change the boundary conditions for the radiative situation, and the walls of the incubator will cool radiativeley faster because of this. There might be a small convective effect but the masses of air involved are not enough for convection to be important.
Now the feeling as if ice radiates cold is just that, a feeling of the faster energy loss of a hand close  to ice.
A: Hot always goes to the lesser degree it is faster depening on  mass    Convection on speed of air has to be considered also  
