what is the temperature equilibrium for a copper conductor conducting 4000 Amps
If you know the viscocity, thermal conductivity and thermal expansivity of the oil, it should be possible to solve the free convection equations from first principles, and so work out at what temperature the power generated in the copper from \$I^2R\$ heating (the easy bit) equals the power lost to the convecting oil (the very hard bit).

However, fun though it may be to set up those flow equations, this is normally done empirically in practice, by measuring temperature rise against current of scale models, and extrapolating from those.

If you do want help solving those flow equations for oil, then you'd be better off on the physics site, it's in no way an electrical problem.