It's established that the nonlinear anomalous Nernst effect (NANE), originating from Berry curvature near the Fermi energy, is symmetry-permitted only when the crystal symmetry in the transport plane of two-dimensional (2D) materials does not exceed a single mirror line. Here, we show that an applied direct electric field can lift this symmetry constraint, enabling an electric-field-induced NANE emerge in time-reversal symmetric 2D systems with higher crystallographic symmetries. This electric-field-induced NANE originates from two contributions: the Berry connection polarization, which roots in the electric-field-corrected Berry curvature, and the anomalous-velocity-modified nonequilibrium Fermi distribution function. Additionally, we propose an alternating temperature gradient as a driving force instead of the conventional steady one, ensuring experimental detection of NANE via second-harmonic measurement techniques. The behaviour of electric-field-induced NANE in the monolayer graphene has been theoretically and systematically investigated.