Temperature compensation lets biochemical clocks keep nearly constant time while the reactions that build them speed up with temperature. This paper asks whether that robustness must be paid for in stochastic timing precision. We study stochastic renewal clocks, in which each tick is the first passage through a productive cycle, and quantify precision by the squared coefficient of variation, $\CV^2$, of the cycle time. A purely sequential Arrhenius clock cannot compensate: some reaction or module must lengthen the period when accelerated. In a canonical single-excursion antagonist, such compensation is possible, but it comes with an exact compensation–coherence trade-off. The trade-off, however, is not fundamental. A chain of $m$ fast two-state entropic gates can compensate while retaining the Erlang-like precision floor $\CV^2\to 1/m$. In this construction, temperature sensitivity is tuned by the enthalpy of an off-pathway state, whereas timing dispersion is set by the number and equilibration of gated stages. For finite gate equilibration, the residual excess variance obeys an exact identity with the dynamical activity, defined as the expected number of directed trap traversals per completed step. Direct finite-generator calculations confirm that these gates flatten the mean period as a function of temperature, not merely the variance. More generally, for order-$n$ Arrhenius phase-type dwells with an activation-energy budget, the compensated timing dispersion has infimum bounded below by the Aldous–Shepp floor $1/n$ and approached from above by an explicit one-trap construction with dispersion $1/(n-1)$; equivalently, the excess cost above the unconstrained phase-type floor is at most $1/[n(n-1)]$. The results apply to stochastic first-passage timing modules and coarse-grained renewal descriptions of biochemical clocks, complementing deterministic limit-cycle theories of temperature compensation. Biologically, the claim is not that KaiC or PER2 is literally a two-state gate, but that multi-state kinetic partitioning can avoid a universal precision penalty by spending internal states and dynamical activity rather than increased steady-state entropy production.