In two-dimensional Fermi liquids (FLs), odd-parity Fermi surface deformations have anomalously slow relaxation rates that are suppressed as T 4 with temperature T, distinct from the standard FL T2 scaling. We demonstrate here that these long-lived modes, which are often hidden in linear response, have a significant impact on nonlinear transport by establishing a direct proportionality of nonlinear thermoelectric currents to the anomalously large relaxation time. These currents exist in topological time-reversal invariant FLs, and their magnitude is characterized by topological heat capacitance terms that we refer to as the Berry curvature capacity and the velocity-curvature capacity. We quantify the effect in bismuth telluride, which is an efficient thermoelectric and a topological insulator with a hexagonal Fermi surface. The proposed field-induced thermoelectric currents are well within the range of current experiments. Our findings demonstrate the potential to explore topological and many-body effects in FLs through the nonlinear thermoelectric response, urging further experimental studies.