Many recipes will tell you to use hot milk when making a bechamel sauce. In fact, I don’t know of anybody who does. Do try not to use milk that has come straight from the refrigerator.
Melt butter in a saucepan and add the butter. Stir to combine. Cook the roux over gentle heat to cook the flour. Remove the saucepan from the heat and add a little of the milk. Stir well, pressing any lumps out with the spoon. Add a little more milk and repeat. You must eliminate the lumps before returning the pan to the heat. When the mixture is smooth, return to heat and cook until it thickens. Remove from heat again and add more milk. Stir vigorously until the sauce is again smooth. If any lumps are left in the sauce in its early stages, they will be almost impossible to remove later. Remember that it is the addition of a cold liquid to a hot base that causes the lumps to form, so the saucepan must always be off the stove when the milk is added. Continue to stir until there are no lumps, add more milk then cook until the sauce reaches the desired consistency. Season with salt and pepper if desired.
Sauce Crème is a white sauce made using some cream to replace some of the milk. Obviously it is richer than béchamel sauce.