[Richard777 (OP)]

The Bohr atom assumes reciprocal forces act upon a bound electron;

“The centripetal force is reciprocal to the electro-static force.”

Assume a modification to the Bohr assumption;

“The magnitude of the centripetal force is equal to the magnitude of the thermo-electric force.”

This assumption combines forces related to heat, electric charge, and momentum. The forces are components of a force vector, the “emissive vector”. Quantization and mass dilation are included in the components.
The emissive vector has three states; a steady state (bound state), a radiant state, and a general state.
If the electric force is equal to zero, the electron is free (unbound).
If various conditions apply, then the orbital radius or black body radiation are easily obtained.
Can heat be included in the Bohr equation?

[Kryptid]

The Bohr model isn't as accurate as quantum mechanics is when it comes to explaining the behavior of atoms. It's also a little tricky to apply temperature to individual subatomic particles. I have seen temperature equated to the kinetic energy (often measured in electronvolts) of subatomic particles, although classically temperature is usually considered an emergent property of bulk systems containing many particles.

[jeffreyH]

It is heat rather than temperature that is considered for inclusion by the poster.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heat.html

[PmbPhy]

The answer to your question Can thermo-electric force be represented as a component of radiation? is no. Radiation (at least the kind you're referring to) is an Electromagnetic wave consisting of an electric field and a magnetic field - period. Nothing else. A force is different than a field. A field doesn't require body to exist whereas a force does. By this I mean that the EM force only exists when there is a charged particle which when placed in an EM field then exist. No charged body to act on -> no force.