The plasma reactor comprises a reaction chamber (23) connectable to a source of ionizable gases (25) and to a heating device (80), said reactor (10) being subjected to the phases of heating (A), cleaning (L) and/or surface treatment (S), cooling (R), unloading (D) and loading (C) of metallic pieces (1). The installation comprises: at least two reactors (10), each being selectively and alternately connected to: the same source of ionizable gases (25); the same vacuum source (60); the same electrical energy source (50); and to the same heating device (80), the latter being displaceable between operative positions, in each of which surrounding laterally and superiorly a respective reactor (10), while the latter is in its heating phase (A) and cleaning phase (L) and/or in the surface treatment phase (S) of the metallic pieces (1).