Temperature ﹩T_{\mathrm{deep}\,}﹩ vs. age for planets with a given M and R. Shown are lines of constant radius for a given mass, labeled by (M/M_J, R/R_J). At a given age, this plot shows the value of ﹩T_{\mathrm{deep}\,}﹩ required to explain a certain mass and radius. There is significant degeneracy between ﹩T_{\mathrm{deep}\,}﹩ and age.