  The distribution of eccentricities e of extra-solar planets with semi-major
axes a > 0.2 AU is very uniform, and values for e are generally large. For a <
0.2 AU, eccentricities are much smaller (most e < 0.2), a characteristic widely
attributed to damping by tides after the planets formed and the protoplanetary
gas disk dissipated. We have integrated the classical coupled tidal evolution
equations for e and a backward in time over the estimated age of each planet,
and confirmed that the distribution of initial e values of close-in planets
matches that of the general population for reasonable tidal dissipation values
Q, with the best fits for stellar and planetary Q being ~ 10^5.5 and ~ 10^6.5
respectively. The current small values of a were only reached gradually due to
tides over the lifetimes of the planets, i.e., the earlier gas disk migration
did not bring all planets to their current orbits. As the orbits tidally
evolved, there was substantial tidal heating within the planets. The past tidal
heating of each planet may have contributed significantly to the thermal budget
that governed the planet's physical properties, including its radius, which in
many cases may be measured by observing transit events. Here we also compute
the plausible heating histories for a few planets with anomalously large
measured radii, including HD 209458 b. We show that they may have undergone
substantial tidal heating during the past billion years, perhaps enough to
explain their large radii. Theoretical models of exoplanet interiors and the
corresponding radii should include the role of large and time-variable tidal
heating. Our results may have important implications for planet formation
models, physical models of "hot Jupiters", and the success of transit surveys.
