 When one of the parameters governing the dynamics of a long-range interacting system of particles in thermal equilibrium is abruptly changed, quenched, to a different value, the system shows a fast relaxation to a non-equilibrium quasi-stationary state, QSS, where the lifetime of such an off-equilibrium state diverges with the system size, and the temperature is non-uniform across the system. The density profile in the QSS obtained after the quenches anti-correlated with the temperature profile in space, exhibiting the phenomenon of temperature inversion. This article was authored by Shamit Gupta and Leipo Cassetti.