[Richard777 (OP)]

Assume a vector of force may represent thermal radiation.

The components of force are associated with energies of heat, light, and matter. The magnitude of thermal force is associated with Plank temperature, and a component of thermal force is associated with Hawking temperature. Components associated with matter give mass dilation. Rest mass is related to the Schwarzschild radius.

Can a vector of force represent thermal radiation?

[evan_au]

Can a vector of force represent thermal radiation?

Thermal radiation (including light, and all other forms of electromagnetic radiation) carries momentum.

If you reflect the electromagnetic radiation, that will apply a force to the mirror. This force will have a magnitude and a direction, so it can be represented as a vector.

This effect is used in solar sails, an active area of investigation for travel within the Solar System, and has even been proposed for sending probes beyond the solar system.
See: https://en.wikipedia.org/wiki/Solar_sail

This requires a greater intensity of light on one side of the sail than the other, or the two forces will cancel out, providing no net force.

thermal force is associated with a ...temperature

A body at a certain temperature emits thermal radiation. If the thermal radiation on one side of a solar sail is more intense than on the other side, then there will be a net force.

But you need something as hot as the Sun (around 5000C) to produce a significant force that you could use to propel a spacecraft, or for satellite station-keeping.

thermal force is associated with Plank temperature

As I understand it, the Planck temperature is a temperature scale (like Fahrenheit, Celsius or Kelvin), which just appeals to some fundamental units.

Just like a Celsius can't exert a force, so a Planck can't exert a force.
See: https://en.wikipedia.org/wiki/Planck_temperature

thermal force is associated with Hawking temperature

A black hole has an effective temperature, due to Hawking radiation. This temperature is certainly related to the Schwarzchild radius of the black hole - the larger the radius, the lower the temperature.

For a black hole the mass of the Sun, this temperature is calculated to be around 60 nanoKelvins.

This means that the Cosmic Background Radiation (with an effective temperature around 2.7 Kelvin) will exert a greater force on a solar sail than the Hawking radiation from a black hole. But both sources of radiation are so weak that the effect would be almost unmeasurable.

See: https://en.wikipedia.org/wiki/Hawking_radiation#Overview