Tidal forces are important for understanding how close binary stars and compact exoplanetary systems form and evolve. However, tides are difficult to model, and significant uncertainties exist about the strength of tides. Here, we investigate tidal circularization in close binaries using a large sample of well-characterized eclipsing systems. We searched TESS photometry from the southern hemisphere for eclipsing binaries. We derive best-fit orbital and stellar parameters by jointly modeling light curves and spectral energy distributions. To determine the eccentricity distribution of eclipsing binaries over a wide range of stellar temperatures (3000-50000K) and orbital separations a/R1 (2-300), we combine our newly obtained TESS sample with eclipsing binaries observed from the ground and by the Kepler mission. We find a clear dependency of stellar temperature and orbital separation in the eccentricities of close binaries. We compare our observations with predictions of the equilibrium and dynamical tides. We find that while cool binaries agree with the predictions of the equilibrium tide, a large fraction of binaries with temperatures between 6250K and 10000K and orbital separations between a/R1~4 and 10 are found on circular orbits, contrary to the predictions of the dynamical tide. This suggests that some binaries with radiative envelopes may be tidally circularized significantly more efficiently than usually assumed. Our findings on orbital circularization have important implications also in the context of hot Jupiters, where tides have been invoked to explain the observed difference in the spin-orbit alignment between hot and cool host stars.