Having a poor track record of making cheese sauces, I'm determined to do it right at least once in this decade. I read that one should use "low heat" only. Too much heat causes the cheese to go stringy or clumpy. Okay - but just what is "low heat"? Warm but not beyond what I can stick my finger in comfortably? Can someone put a number on it, degrees centigrade?
In a cooking instruction, "low heat" doesn't refer to the temperature the sauce reaches, but the speed at which you heat it up. Many stove rings (hobs) are marked min-2-3-4-med-6-7-8-max. On that scale, a low heat would be 2 or 3. Very low heat would be min or 2. Left on the stove long enough, even at min, your sauce will boil. The key about using low heat is that it probably won't boil in the amount of time you need to melt the cheese, and that's good.
I make cheese sauce regularly (did so tonight) and I start at med to melt the butter, turn it down while the roux cooks, add milk, once it's pretty thick I turn it down even further, or just turn it off since an electric element will hold heat for a while, then stir in the cheese. If it ever happened that my cheese wasn't melting I guess I would turn the heat back up a bit, but that hasn't happened to me.
Cheese have enzymes. Enzymes break quickly and easily at 150F/65 C. 50 Celsius for a short period of time should suffice to melt you cheese without breaking the protein structures.
I have committed the same mistake many times. Actually the fist day my in laws where over i tried to impress them with homemade pasta and cheese sauce. My Cheese sauce clumped. My back up plan is to add milk tomato sauce put it on the blender until it liquifies.