Temperature profiles of the first and the second moment of the nematic order parameter distribution function, as determined from the deuteron nuclear magnetic resonance line shapes, as well as heat capacity response, provide support for the supercritical scenario of the nematic-paranematic phase transition in liquid single crystal elastomers. The relative strength of the locked-in internal mechanical field with respect to the critical field can be decreased by swelling the elastomer samples with low molecular mass nematogen. By increasing the concentration of the dopant, critical and below-critical behavior is promoted.