The primary challenges for simulating a turbulent flow over a micro‐structured surface arise from the two hugely disparate spatial length scales. For fluid–solid coupled conjugate heat transfer (CHT), there is also a time‐scale disparity. The present work addresses the scale disparities based on a two‐scale framework. For the spatial scale disparity, a dual meshing is employed to couple a global coarse‐mesh domain with local fine‐mesh blocks around micro‐structures through source terms generated from the local fine‐mesh and propagated to the global coarse‐mesh domain. The convergence and robustness of the source terms driven coarse‐mesh solution is enhanced by a balanced eddy‐viscosity damping. In this work, the two‐scale method previously developed only for a fluid‐domain is extended to a solid domain so that thermal conduction around micro‐elements can now be resolved accurately and efficiently. The fluid–solid timescale disparity is dealt with by a frequency domain approach. The time‐averaged (zeroth harmonic) is effectively obtained in the same way as steady CHT. And remarkably, wall temperature unsteadiness can be simply obtained from the fluid temperature harmonics through a wall fluid–solid temperature harmonic transfer‐function at minimal computational cost. The developed CHT capability is validated for an experimental internal cooling channel with multiple surface rib‐elements. For a test configuration with 100 micro‐structures, the fluid domain‐only, the solid domain‐only and the fluid–solid coupled CHT solutions are analyzed respectively to examine and demonstrate the validity of the present framework and implementation methods. Some of the results also serve to illustrate the primary underlying working of the methodology. The two‐scale method previously developed for turbulent flow solution is extended to a solid domain, enabling LES conjugate heat transfer solutions for micro‐structured surface. The wall temperature unsteadiness is resolved efficiently through a harmonic transfer function. The method is validated against experimental data. The two‐scale capability indicates the potential for the cost of conjugate heat transfer solutions for micro‐structured surfaces to be largely independent of the number of microstructure elements.