This temperature target is really just to begin killing weed seeds - it takes a sustained temp above 140F/60C to begin killing pathogenic bacteria, with ~160F/71C being required to get to the most tenacious. If all that’s being composted is grass and garden waste and leaves and wood chips then by all means aim for 120F/49C but if the pile incorporates manures or carcasses then 160F/71C should be the target temperature.