The process of curing the acrylic oligomers for rapid thermal curing coatings in the presence of hexa(methoxymethyl)melamine (HMMM), tetra(butoxymethyl)glycoluril (TBMG), and tetra(methoxymethyl)glycoluril (TMMG) has been studied. When HMMM is used as a hardener, the content of hydroxyl groups in the terpolymer and also the crosslinking agent concentration have little effect on the initial cure rate. It has been established that during the curing of the TMMG composition, the amount of the network polymer and the initial curing rate decrease at short curing times only. It has also been revealed that the use of butoxy groups instead of methoxy groups as blocking agents leads both to a decrease in the initial cure rate and the gel fraction limiting value from 98 to 80%. When it comes to TBMG-containing compositions, a decrease in the part of hydroxyl groups in the copolymer leads to a significant fall in the initial curing rate and also in the gel fraction content. Regardless of the crosslinking agent used, an acceleration of the curing process is observed with an increase in the catalyst content in the compositions.