Nonequilibrium interface phenomena play a key role in crystallization, hydrate formation, pipeline depressurization, and a multitude of other examples. Square gradient theory extended to the nonequilibrium domain is a powerful tool for understanding these processes. The theory gives an accurate prediction of surface tension at equilibrium, only with temperature-dependent influence parameters. We extend in this work the nonequilibrium square gradient model to have temperature-dependent influence parameters. The extension leads to thermodynamic quantities which depend on temperature gradients. Remarkably the Gibbs relation proposed in earlier work is still valid. Also for the extended framework, the "Gibbs surface" described by excess variables is found to be in local equilibrium. The temperature-dependent influence parameters give significantly different interface resistivities (∼9%-50%), due to changed density gradients and additional terms in the enthalpy. The presented framework facilitates a more accurate description of transport across interfaces with square gradient theory.