If the temperatures are equal they radiate equal amounts of energy to each other. No radiation cancels. See the references below.
Classical physics has known about radiation physics for about a century.
There are many references about EM radiation fields that disagree with you. Some are cited below. The first two say that radiation is still exchanged when the temperatures are the same. The third reference says that radiation is being exchanged, no matter what the temperature difference is.
http://en.wikipedia.org/wiki/Radiative_equilibrium
Planck (1914) refers to a condition of thermodynamic equilibrium, in which "any two bodies or elements of bodies selected at random exchange by radiation equal amounts of heat with each other."
http://quantummechanics.ucsd.edu/ph130a/130_notes/node48.html
"A black body is one that absorbs all the EM radiation (light...) that strikes it. To stay in thermal equilibrium, it must emit radiation at the same rate as it absorbs it ...".
http://en.wikipedia.org/wiki/Thermal_equilibrium
"One form of thermal equilibrium is radiative exchange equilibrium. Two bodies, each with its own uniform temperature, in solely radiative connection, no matter how far apart, or what partially obstructive, reflective, or refractive, obstacles lie in their path of radiative exchange, not moving relative to one another, will exchange thermal radiation, in net the hotter transferring energy to the cooler, and will exchange equal and opposite amounts just when they are at the same temperature"
How can you argue against all that and still maintain you understand radiation physics more than what is taught in physics courses? There is even a phrase in physics , "radiative exchange equilibrium," which is contrary to your post.
