We investigated the paranematic-to-nematic phase transition of nematic main-chain liquid single-crystal elastomers by means of high-resolution ac calorimetry and deuteron quadrupole-perturbed nuclear magnetic resonance. We determined that the cross-linking density strongly affects the thermodynamic response of the system, driving the transition from first order to supercritical via critical point of liquid-vapor type. This result together with recent findings in side-chain liquid crystal elastomers support the universality of such thermodynamic behavior in liquid crystal elastomers. Furthermore, the impact of frozen-in mechanical field during the preparation of samples has been systematically explored in this work. It is shown that the critical behavior can be controlled by both cross-linkers-induced internal random mechanical fields and frozen-in uniform mechanical field applied externally.