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 dynamics, 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 on a 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 flows in the direction of the gradient of temperature; and to identify regions of parameters corresponding to a negative thermal conductivity (i.e. a positive linear response to a gradient of temperature). The agreement with previous results obtained by numerical simulation of the microscopic physical system confirms the validity of the macroscopic equations we derive.