Did General relativity Field Equation take temperature & magnetisn in the space of the Universe into account?

Answer 1

Magnetism, yes. Temperature, no. Temperature, as such, has no effect on the structure of space-time. The motion of atoms and other particles can be included in the field equations, but is usually omitted unless the speeds are very large. Temperature is the random motion of atoms, ions, molecules, etc.

Answer 2

Your previous answer is wrong.

Magnetism is a special relativistic effect (it arises from a relativistic correction to the electsonstatic force).

Temperature - yes. The Stress Energy tensor implicity expresses both the mass and energy in a volume of spacetime. The energy element is important because, of course, if the mass is moving then it needs correction under special relativity. Temperature is movement of mass (in the most general terms).