Although multi-branch horizontal well coalbed methane (CMB) extraction has been comprehensively investigated, fewer scholars have taken the effect of temperature into account, which brought a large deviation for the study of multi-branch horizontal well parameter design. In this work, the hydraulic-mechanical-thermal coupled model of multi-branch horizontal well CMB extraction was established. In order to verify the accuracy of the model and study the effect of temperature on CMB extraction, a series of numerical simulations based on engineering geological conditions and drilling arrangement parameters of 24307 face of Shaqu Mine were made, results show that: The CH4 production rate of both field data and numerical simulation result have the same changing tendency, and the difference between the simulation result and the actual value is not big. In multi-branch horizontal well CMB extraction process, the matrix shrinkage caused by temperature reduction and methane desorption dominates, the permeability continues to increase. Due to the effect of temperature on the amount of gas adsorbed by coal, the CH4 production decreases with the increase of initial reservoir temperature, and the permeability of coalbed increases with the increase of temperature.