We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial differential equations with boundary conditions determined by the thermo-mechanical forcing. Instead of expensive Monte Carlo simulations of the underlying microscopic physical system, we perform extensive numerical simulations based on a finite difference method for the system of partial differential equations describing the macroscopic steady state. We first present a formal derivation of these stationary equations based of linear response argument and local equilibrium assumptions. We then study various properties of the solutions to these equations. This allows to characterize the regime of parameters leading to uphill diffusion, a situation where the energy flux flows in the direction of the gradient of temperature; and to identify regions of parameters where a negative thermal conductivity is observed. The agreement with previous results made by numerical simulation of the microscopic dynamics confirm the validity of these macroscopic equations.