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To explain their observed radii, we present theoretical radius-agetrajectories for the extrasolar giant planets (EGPs) TrES-4, XO-3b, andHAT-P-1b. We factor in variations in atmospheric opacity, the presence of aninner heavy-element core, and possible heating due to orbital tidaldissipation. A small, yet non-zero, degree of core heating is needed to explainthe observed radius of TrES-4, unless its atmospheric opacity is significantlylarger than a value equivalent to that at 10$\times$solar metallicity withequilibrium molecular abundances. This heating rate is reasonable, andcorresponds for an energy dissipation parameter ($Q_p$) of $\sim10^{3.8}$ to aneccentricity of $\sim$0.01, assuming 3$\times$solar atmospheric opacity and aheavy-element core of $M_c = 30$ $M_{\oplus}$. For XO-3b, which has an observedorbital eccentricity of 0.26, we show that tidal heating needs to be taken intoaccount to explain its observed radius. Furthermore, we reexamine the core massneeded for HAT-P-1b in light of new measurements and find that it now generallyfollows the correlation between stellar metallicity and core mass suggestedrecently. Given various core heating rates, theoretical grids and fittingformulae for a giant planet's equilibrium radius and equilibration timescaleare provided for planet masses $M_p=$ 0.5, 1.0, and 1.5 $M_J$ with $a =$0.02-0.06 AU, orbiting a G2V star. When the equilibration timescale is muchshorter than that of tidal heating variation, the ``effective age'' of theplanet is shortened, resulting in evolutionary trajectories more like those ofyounger EGPs. Motivated by the work of \citet{jackson08a,jackson08b}, wesuggest that this effect could indeed be important in better explaining someobserved transit radii.

Theoretical Radii of Extrasolar Giant Planets: the Cases of TrES-4, XO-3b, and HAT-P-1b