We investigated extensively equilibrium, nonequilibrium, and nonlinear aspects of the enthalpy relaxation in a supercooled liquid [Ca(NO3)(2)](0.4)(KNO3)(0.6). The equilibrium properties of relaxation, which are described in the framework of linear response theory, were determined from the frequency-dependent heat capacity measurements. The nonequilibrium and nonlinear aspects of relaxation were investigated by differential scanning calorimetry and time-domain dynamic calorimetry. It was found that the nonequilibrium relaxation can be fully accounted for in terms of the equilibrium one if the latter is properly extended, and that the successful extension of the equilibrium linear relaxation function must include both nonstationariness and thermorheological complexity. No evidence of genuine nonlinear enthalpy response, aside from the nonequilibrium effects, was seen in the time-domain dynamic calorimetric data, even when a temperature jump as large as 8 K was imposed.