account the full nature of the tidal equations severely modifies the planet’s tidal and thermal evolution, compared with the aforementioned truncated calculations, leading to significantly different tidal heat rates and thus planet contraction rates.

After introducing our model in §\[sec:hyp\], we examine in detail in §\[sec:q\] the relation between the *constant time lag* ($\Delta t$) in Hut’s (and thus our) model and the usual tidal quality factor ($Q$) widely used in the literature. Constraints on $\Delta t$ from the study of the galilean satellites are also derived. In §\[sec:2ndOrder\], we demonstrate, with [*analytical arguments*]{}, that truncating the tidal equations at $2^{\mathrm{nd}}$ order in eccentricity leads to wrong tidal evolution histories, with sequences drastically differing from the ones obtained when solving the complete equations. In §\[sec:comp\], we compare our full thermal/orbital evolution calculations with similar studies based on a truncated and constant $Q$ tidal model. These numerical comparisons confirm and quantify the conclusions reached in §\[sec:2ndOrder\], namely that low order eccentricity models substantially underestimate the tidal evolution timescales for initially eccentric systems and thus lead to incorrect tidal energy contributions to the planet’s energy balance. For instance, we show that tidal heating can not explain the radius of HD 209458b, for 