A degree of frost is a non-standard unit of measure for air temperature meaning degrees below melting point (also known as "freezing point") of water (32 degrees Fahrenheit or 0 degrees Celsius). "Degree" in this case can refer to degree Celsius or Fahrenheit.
When based on Celsius, 0 degrees of frost is the same as 0°C, and any other value is simply the negative of the Celsius temperature. When based on Fahrenheit, the conversion is a bit more complicated, as 0 degrees of frost is equal to 32°F. Conversion formulas:
Beurre monté refers to melted butter that remains emulsified, even at temperatures higher than that at which butter usually breaks down. Beurre monté may refer either to the melted butter sauce itself, or to the method of making it.
Butter is an emulsion of about 2% milk solids, 80% milk fats (clarified butter), and about 18% water. At 160 degrees Fahrenheit (71 degrees Celsius), butter normally breaks down into its components parts. But in a beurre monté, the butter is heated in such a way that the butter can stay emulsified even up to 180 or 190 degrees Fahrenheit (82 to 88 degrees Celsius). It can then be used in many ways, including as a sauce, as an ingredient for other sauces, as a poaching medium, or as a resting medium for cooked meat.