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 Creme Sauce Crème is a white sauce made using some cream to replace some of the milk. Obviously it is richer than béchamel sauce.
White sauce is the generic name for a whole collection of sauces having one thing in common: they are based on a roux of equal weights of butter and flour. They are called white sauces because the roux is not coloured and the resulting sauce remains white. It is the liquid that usually varies in white sauces. Technically, the sauce we know as white sauce is actually bechamel sauce, the liquid used being milk. With all white sauces the proportions are 50g butter, 50g flour and 600ml liquid to give 600ml of sauce. In all white sauces it is important to fry the roux gently to ‘cook’ the flour. This breaks up the gluten content of the flour and ensures that the resulting sauce does not have a floury taste that no amount of cooking will remove later.