I would like to know whether the reaction will take place if glycerol and citric acid are merged? In particular, what will happen if both substances are heated up to high temperature (+100°C)?
As @Mithoron said, it will form esters. Actual name is Citric acid esters of tri-glycerides or citroglycerides.
Where at least one of R1, R2 or R3 represents a citric acid moiety, one represents a fatty acid moiety and the remainder may represent citric acid, fatty acid or hydrogen.
Obtained by esterification of glycerol with citric acid [...] acid; consists of mixed esters of citric acid and edible fatty acids with glycerol; may contain minor parts of free fatty acids, free glycerol, free citric acid and mono- and diglycerides; may be wholly or partially neutralized with sodium hydroxide or potassium hydroxide.
They are white to ivory coloured, oily to waxy material. They are used as stabilizer, emulsifier, dough conditioner, antioxidant synergist.
The influence of various heating methods without catalysis to prepare polyesters from citric acid : glycerol blends were studied. In the presence of short-term microwave treatments, i.e., 60 s at 1200 W, blends of glycerol and citric acid invariably formed solid amorphous polyesters. Fourier transform infrared spectroscopy showed that citric acid and glycerol blends can form highly stable polymers composed of ester bonds. The glycerol citrate polyester polymers exhibited the least degradation in water, more in acid solutions (0.1–1.0M HCl), and the most deterioration in strong alkaline solutions (0.1–1.0M NaOH) after 72 h soakings. Polyesters of glycerol and citric acid were studied with differential scanning calorimetry and thermal gravimetric analysis. The polyesters were found to be thermally stable (up to 313°C).
A noble application of glycerol + citric acid esters or citroglycerides is in the making of a biodegradable thermoset polymers.
A new biodegradable thermoset polymer, was made from simple, economical, biocompatable monomers without the need for a catalyst. Glycerol and citric acid, non-toxic and renewable reagents, were crosslinked by a melt polymerization reaction at temperatures from 90-150°C. Consistent with a condensation reaction, water was determined to be the primary byproduct. The amount of crosslinking was controlled by the reaction conditions, including temperature, reaction time, and ratio between glycerol and citric acid. Also, the amount of crosslinking was inversely proportional to the rate of degradation. [...]
The notable increase in global consumption of plastics and their long residence time in the atmosphere show the great need for biodegradable products. In this project, we developed biodegradable polymers based on citric acid and glycerol. Their synthesis was carried out at different conditions of constant temperature and concentration and they were synthesized using an economically viable method. Characterization was undertaken using: Acid number, FTIR spectroscopy, refractive index, viscosity, impact analysis, tensile test, hardness, calorimetry, the % humidity (oven method with recirculating air), and density determination, along with qualitative evidence to corroborate their biodegradability. These elaborated polymers were mixed with medical grade PVC formulation, obtaining a hybrid polymer, showing their mechanical properties were changed.