A process for the production of a thermoset polyester foam, comprising the following successive steps: (a) heating an essentially anhydrous pre-oligomerization composition, containing - a polyol component comprising at least 30% by weight of hydrogenated sugar selected from hydrogenated sugars of formula C n H 2n+2 O n in which n is 4, 5 or 6, - a polyacid component comprising a pore-forming polyacid preferably chosen from citric acid and α-hydroxylated dicarboxylic acids of formula HOOC-(CHR 1) n -CHOH-COOH in which n is an integer ranging from 1 - 4, preferably from 1 - 3, in particular 1 or 2 and very particularly preferably 1, and each R 1 independently represents a hydrogen atom, a hydroxyl (-OH) group or an alkyl group, preferably a C 1-4 alkyl group, and - a catalyst, said pre-oligomerization composition containing less than 1 % by weight of glycerol, at a temperature of between 100°C and less than 160°C for a duration of between 10 and 60 minutes, preferably between 15 and 40 minutes, with mechanical stirring, so as to react the polyol component with the polyacid component and form a composition of oligomeric esters, (b) incorporating a surfactant composition into the composition of oligomeric esters, so as to obtain a thermosetting expandable composition, (c) introducing the resulting thermosetting expandable composition into a mold or applying the resulting thermosetting expandable composition to a support, (d) heating the thermosetting expandable composition at a temperature at least equal to 160°C, preferably between 165°C and 185°C, for a duration of between 10 minutes and 8 hours, preferably between 20 minutes and 7 hours and in particular between 30 minutes and 6 hours, so as to form a thermoset polyester foam. (a) heating an essentially anhydrous pre-oligomerization composition, containing - a polyol component comprising at least 30% by weight of hydrogenated sugar selected from hydrogenated sugars of formula C n H 2n+2 O n in which n is 4, 5 or 6, - a polyacid component comprising a pore-forming polyacid preferably chosen from citric acid and α-hydroxylated dicarboxylic acids of formula HOOC-(CHR 1) n -CHOH-COOH in which n is an integer ranging from 1 - 4, preferably from 1 - 3, in particular 1 or 2 and very particularly preferably 1, and each R 1 independently represents a hydrogen atom, a hydroxyl (-OH) group or an alkyl group, preferably a C 1-4 alkyl group, and - a catalyst, said pre-oligomerization composition containing less than 1 % by weight of glycerol, at a temperature of between 100°C and less than 160°C for a duration of between 10 and 60 minutes, preferably between 15 and 40 minutes, with mechanical stirring, so as to react the polyol component with the polyacid component and form a composition of oligomeric esters, - a polyol component comprising at least 30% by weight of hydrogenated sugar selected from hydrogenated sugars of formula C n H 2n+2 O n in which n is 4, 5 or 6, - a polyacid component comprising a pore-forming polyacid preferably chosen from citric acid and α-hydroxylated dicarboxylic acids of formula HOOC-(CHR 1) n -CHOH-COOH in which n is an integer ranging from 1 - 4, preferably from 1 - 3, in particular 1 or 2 and very particularly preferably 1, and each R 1 independently represents a hydrogen atom, a hydroxyl (-OH) group or an alkyl group, preferably a C 1-4 alkyl group, and n is an integer ranging from 1 - 4, preferably from 1 - 3, in particular 1 or 2 and very particularly preferably 1, and each R 1 independently represents a hydrogen atom, a hydroxyl (-OH) group or an alkyl group, preferably a C 1-4 alkyl group, and - a catalyst, (b) incorporating a surfactant composition into the composition of oligomeric esters, so as to obtain a thermosetting expandable composition, (c) introducing the resulting thermosetting expandable composition into a mold or applying the resulting thermosetting expandable composition to a support, (d) heating the thermosetting expandable composition at a temperature at least equal to 160°C, preferably between 165°C and 185°C, for a duration of between 10 minutes and 8 hours, preferably between 20 minutes and 7 hours and in particular between 30 minutes and 6 hours, so as to form a thermoset polyester foam.