Blender sun settings are separate from the LiVi Context settings.
If you want to set 1366W/m2 then look up the use of Radiance's gensky command to generate the sun description with the desired intensity. You can then replace the LiVi Context sky description with the gensky output with a Text Edit node.
LiVi won't calculate thermals though. Ole is correct, you can use an editor to replace the solar intensity in an hourly EPW file for thermal analysis with EnVi/EnergyPlus but EnergyPlus is designed to model buildings and you would have to make other changes to make the sun position constant and to eliminate convection from your calculations. Your metal box would also need to hollow like a room. All of this takes EnergyPlus out of the realm it was designed for however, and the mathematical assumptions it uses may become invalid. You would probably be better off with some kind of finite element analysis tool. LiVi could be used to generate the radiation boundary conditions for such a model, but if it's just a box you could calculate incident radiation based on angle of incidence quite easily without it.
In short, good luck but it will take some work to get EnergyPlus to do it, even if it can, and there would be no guarantee that the results are realistic.