The process of extracting coalbed methane (CBM) is not only of significance for unconventional energy supply but also important in mine safety. The recent advance in fracking techniques, such as carbon dioxide (CO2) fracking, intensifies the complexity of stimulated coalbeds. This work focuses on developing a fully coupled multidomain model to describe and get insight into the process of CBM extraction, particularly from those compound-fractured coalbeds. A group of partial differential equations (PDEs) are derived to characterize gas transport from matrix to fractures and borehole. A stimulated coalbed is defined as an assembly of three interacting porous media: matrix, continuous fractures (CF) and radial primary hydraulic fracture (RF). Matrix and CF constitute a dual-porosity-dual-permeability system, while RF is simplified as an 1-D cracked medium. These media further form three distinct domains: non-stimulated reservoir domain (NSRD), stimulated reservoir domain (SRD) and RF. The effects of coal deformation, heat transfer, and non-thermal sorption are coupled into the model to reflect the multiple processes in CBM extraction. The finite element method is employed to numerically solve the PDEs. The proposed model is verified by comparing its simulation results to a set of well production data from Southern Qinshui Basin in Shanxi Province, China. Great consistency is observed, showing the satisfactory accuracy of the model for CBM extraction. After that, the difference between various stimulation patterns is presented by simulating the CBM extraction process with different stimulation patterns including (1) unstimulated coalbed; (2) double-wing fracture + NSRD; (3) multiple RFs + NSRD; (4) SRD + NSRD and (5) multiple RFs + SRD + NSRD. The results suggest that Pattern (5) (often formed by CO2 fracking) boosts the efficiency of CBM extraction because it generates a complex fracture network at various scales by both increasing the number of radial fractures and activating the micro-fractures in coal blocks. Sensitivity analysis is also performed to understand the influences of key factors on gas extraction from a stimulated coalbed with multiple domains. It is found that the distinct properties of different domains originate various evolutions, which in turn influences the CBM production. Ignoring thermal effects in CBM extraction will either overestimate or underestimate the production, which is the net effect of thermal strain and non-isothermal sorption. The proposed model provides a useful approach to accurately evaluate CBM extraction by taking the complex evolutions of coalbed properties and the interactions between different components and domains into account. The importance of multidomain and thermal effects for CBM reservoir simulation is also highlighted.