We present a comprehensive molecular-dynamics study of Doppler laser cooling for ${}^{88}\mathrm{Sr}^{+}$ Coulomb crystals ($N=50$) confined in a linear Paul trap with controlled structural phase transitions. By varying the end-cap voltage $U_{\mathrm{EC}}$ from 0.5 to 100 V (Mathieu $q=0.2$), we investigate the temperature evolution across the linear, zigzag, and ellipsoid structures. Instead of a single global temperature, we employ energy decomposition thermometry to separate the secular ($T_{\sec }$) and micromotion ($T_{\mathrm{MM}}$) contributions, and find that micromotion accounts for 60–99% of the total kinetic energy along the whole structural sequence, exceeding 99% in the ellipsoid phase. Binned spatial statistics over five independent runs reveal only weak radial correlations of the secular temperature (fitted slopes between $-0.22$ and $+0.03 \mathrm{mK}/\mu \mathrm{m}, R^2=0.17–0.64$) with an absolute radial variation below 6 mK, whereas the coherent micromotion follows $T_{\mathrm{MM}}\propto r^2$ with $R_{\mathrm{quad}}^2=0.993$ and reaches ${10}^3\mathrm{mK}$ at the crystal periphery: the crystal thus combines a radially homogenized secular temperature with a strongly position-dependent micromotion amplitude. The axial secular component stays at 1–5 mK, at or a few times above the Doppler limit, at every voltage because it is directly laser cooled, while the transverse components are heated to 4–6 mK in the ellipsoid phase. The crystal is therefore transversely isotropic but remains axially and radially anisotropic. Control simulations in which the rf drive is replaced by its pseudopotential equivalent show that micromotion-induced Coulomb heating supplies about 60% of the secular kinetic energy in the ellipsoid phase, whereas the two configurations agree to within 10% in the linear chain; the micromotion energy is always present, but it is converted into secular motion only in multidimensional crystals. A transverse anisotropy of about 30% between $T_x$ and $T_y$ appears in the zigzag regime and weakens in ellipsoids. These findings demonstrate that global averages measure a thermally averaged secular energy dominated by micromotion-induced Coulomb heating rather than local secular temperature variations, with important implications for quantum gate fidelity in scalable ion trap architectures.

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• Ab initio molecular dynamics
• Atom & ion cooling
• Atom & ion trapping & guiding