We investigate the heat conductivity $kappa$ of the Heisenberg spin-1/2 ladder at finite temperature covering the entire range of inter-chain coupling $J_perp$, by using several numerical methods and perturbation theory within the framework of linear response. We unveil that a perturbative prediction $kappa propto J_perp^{-2}$, based on simple golden-rule arguments and valid in the strict limit $J_perp to 0$, applies to a remarkably wide range of $J_perp$, qualitatively and quantitatively. In the large $J_perp$-limit, we show power-law scaling of opposite nature, namely, $kappa propto J_perp^2$. Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at $J_perp = J_parallel$. As a function of temperature $T$, this minimum scales as $kappa propto T^{-2}$ down to $T$ on the order of the exchange coupling constant. These results provide for a comprehensive picture of $kappa(J_perp,T)$ of spin ladders.
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