The mechanism-first fix
Keep the heat low and take it off the burner to melt
Casein clumps past a real temperature threshold, not a
vague one. Melting off direct heat, or on a slow cooker's lowest
setting, keeps the sauce under that line.
What to do: pull the pan off the burner (slow
cooker to low, not high) before the cheese goes in, and stir it
through residual heat, not active heat.
Documented, not our own number
30 recipes grate
their own
Grate your own cheese for standard insurance
Every other page on this question leads with this, and
outside documentation backs the mechanism, even though our own
comparison couldn't confirm a smoothness difference directly.
What to do: buy a block, grate it yourself, toss
it with a spoonful of the dry pasta before it hits the sauce.