As a clean energy resource, coalbed methane (CBM) has drawn worldwide attention. However, the CBM reservoir has strong adsorption capacity and low permeability and thus requires stimulation. Realized by the conversion of the electromagnetic energy into the thermal energy, microwave heating may be a sound stimulation method. In this study, the effect of microwave heating on the petrophysical characteristics of coal was investigated by combining modelling, experiment and analysis. The numerical model coupled the electromagnetic and heat transfer physics by the thermal-dependent coal permittivity. The results indicate that the increase in the microwave power contributes not only to rapid heating but also to thermal heterogeneity. The Nuclear Magnetic Resonance (NMR) tests show that microwave heating can induce the enlargement, opening and interconnection of pores and fractures in coal. Furthermore, the NMR multifractal theory was proposed for quantitative pore structure characterization. The calculated adsorption fractal dimension increases with the temperature, while the seepage fractal dimension shows a positive linear correlation with the thermal heterogeneity. Outcomes of this study provide valuable insight into microwave-assisted CBM recovery. (C) 2019 Elsevier B.V. All rights reserved.