Dimensionally reduced QCD at high temperature

Finite-temperature QCD at high temperature T exhibits three different momentum scales T,gT and g2T. Naive perturbation theory in a small gauge coupling g does not work beyond leading order. In the framework of effective theories, a separation of contributions originating from the different momentum scales can be systematically performed, allowing for higher-order weak-coupling expansions. In this talk, we review finite-temperature QCD in the EQCD/MQCD framework, and outline a specific high-precision calculation of matching coefficients therein.