NOVELTY - Pyrolytic thermal fractionation of microalgae biomass comprising a protein component, a carbohydrate component, and a triglyceride component, comprises heating the microalgae biomass to a first volatilization temperature of a first component comprising protein materials, then to a second volatilization temperature of a second component comprising carbohydrate materials, and finally to a third volatilization temperature of a third component comprising triglycerides; and removing and recovering the first, second, and third volatilized compound.    USE - The methods are used for pyrolytic thermal fractionation of microalgae biomass comprising a protein component, a carbohydrate component, and a triglyceride component; and fatty acid alkyl ester production (all claimed).    ADVANTAGE - Thermal fractionation of biomass of non-lignocellulosic origin for multiple high-quality biofuels is provided.    DETAILED DESCRIPTION - Pyrolytic thermal fractionation of microalgae biomass comprising a protein component, a carbohydrate component, and a triglyceride component, comprises (a) heating the microalgae biomass to a first volatilization temperature of a first component comprising protein materials, and holding the first volatilization temperature of the heated microalgae biomass constant for a first period of time until no further mass loss of the first component occurs, thus producing a first volatilized compound derived from the protein materials, where the first volatilization temperature is 180-240 degrees C; (b) removing and recovering the first volatilized compound from the microalgae biomass remaining from step (a); (c) heating the microalgae biomass remaining from step (b) to a second volatilization temperature of a second component comprising carbohydrate materials, and holding the second volatilization temperature of the heated microalgae biomass constant for a second period of time until no further mass loss of the second component occurs, thus producing a second volatilized compound derived from the carbohydrate materials, where the second volatilization temperature is 300-350 degrees C; (d) removing and recovering the second volatilized compound from the microalgae biomass remaining from step (c); (e) heating the microalgae biomass remaining from step (d) to a third volatilization temperature of a third component comprising triglycerides, and holding the third volatilization temperature of the heated biomass constant for a third period of time until no further mass loss of the third component occurs, thus producing a third volatilized compound derived from the triglycerides, where the third volatilization temperature is 370-480 degrees C; and (f) removing and recovering the third volatilized compound from the microalgae biomass remaining from step (e). An INDEPENDENT CLAIM is a method of fatty acid alkyl ester production by (a) heating a microalgae biomass comprising a protein component, a carbohydrate component, and a triglyceride components to a first volatilization temperature of a first component comprising protein materials, and holding the first volatilization temperature of the heated microalgae biomass constant for a first period of time until no further mass loss of the first component occurs, thus producing a first volatilized compound derived from the protein materials, where the first volatilization temperature is 180-240 degrees C; (b) removing and recovering the first volatilized compound from the microalgae biomass remaining from step (a); (c) heating the microalgae biomass remaining from step (b) to a second volatilization temperature of a second component comprising carbohydrate materials, and holding the second volatilization temperature of the heated biomass constant for a second period of time until no further mass loss of the second component occurs, thus producing a second volatilized compound derived from the carbohydrate materials, where the second volatilization temperature is 300-350 degrees C; (d) removing and recovering the second volatilized compound from the microalgae biomass remaining from step (c); (e) heating the microalgae biomass remaining from step (d) to a third volatilization temperature of a third component comprising triglycerides, and holding the third volatilization temperature of the heated biomass constant for a third period of time until no further mass loss of the third component occurs, thus producing a third volatilized compound derived from the triglycerides, where the third volatilization temperature is 370-480 degrees C; (f) removing and recovering the third volatilized compound from the microalgae biomass remaining from step (e); and (g) esterifying the third volatilized compound to produce one or more of: fatty acid alkyl esters and biodiesel.