How is heat transferred in a two-dimensional vacuum field?

[Olias]

How does HEAT, get transferred form one location to another in only a two-dimensional field?

If we define the Cold Vacuum of space as a field background(I believe current models define Einsteins field Eqautions as being Vacua dominant), just how does thermal Heat move across Space?

 

[Integral]

Heat conduction in materials is governed by the heat equation:

u_t = u_{xx}+u_{yy}

In free space or even still air the main mechanism for heat transfer is Radiation. Seems to me that the energy goes like

E= \sigma \Delta T^4

here \sigma is the Stephan Boltzmann constant.