Microchannel cooling is often the preferred choice for compact heat sinks. However, widely adopted topology optimisation (TO) techniques such as density-based and level-set methods often struggle to generate very thin channel strips unless maximum length scale constraints are imposed and very fine meshes are employed. To address this limitation, multi-scale design methodologies have emerged. This paper builds upon recent advances in de-homogenisation techniques to contribute to the multi-scale design of microchannels for cooling applications. We start by selecting a single-class microstructure and employ numerical homogenisation to build an offline library. This library is then fed in online macro-scale topology optimisation, where both microstructure parameters and local orientation fields are optimised. By using a sawtooth-function-based mapping, the de-homogenised results capture fine details across different length scales through a unique homogenised design. Our findings show that the generated microchannels outperform conventional pillar arrays, offering valuable insights for heat sink designers. Additionally, imperfections observed in the de-homogenised results serve as benchmarks for future improvements, addressing concerns related to modelling accuracy, manufacturability, and overall performance enhancements.