This invention is a method of making and polymer of heat resistant polyester, being characterized by the reaction product of a polyester which consists of the aromatic dicarboxylic acid and a glycol with 2-6 carbons reacted with 0.2-5 weight % of a bifunctional epoxy compound which is expressed by the general formula ##STR1## wherein R is benzene ring, naphthalene ring, cyclohexane ring, cyclohexene ring or pyridine ring; and R may have a substitution group to keep the amount of the end carboxyl groups below 15 gram equivalents per 10.sup.6 grams of polymer.