Poly(lactic acid) (PLA) copolymers having a significantly higher glass transition temperature (T-g) than that of high molar mass PLA homopolymers (typically 60 +/- 5 degrees C) were prepared. Lactic acid was copolymerized with 1,4:3,6-dianhydro-D-glucitol (isosorbide, ISB) and succinic acid (SA-2), 1,2,3,4-butanctetracarboxylic acid (BTCA-4) or 1,2,3,4,5,6-cyclohexanehexacarboxylic acid (HCA-6). The highest T(g)s obtained for the copolymers containing BTCA-4 and HCA-6 were 80 and 86 degrees C, respectively. The polymers were prepared by step-growth polymerization in the melt phase, which is an easily operable and simple PLA production method in comparison to the ring-opening polymerization (ROP) route. It was shown that the T-g and the cross-linking induced by the polyfunctional carboxylic acid comonomers could be readily controlled by choosing a suitable polymerization time and temperature. Similar improvement in the T-g as achieved for the copolymers of BTCA-4 and HCA-6 was not observed for linear copolymers containing ISB and SA-2.