Under high-temperature conditions, heat evacuation of foil bearing has a significant impact on bearing performance, including loading performance and reliability. During bearing operation, viscous dissipative heat in the lubricant gas film is the main source of heat generation. For foil bearings, enhancing the heat evacuation efficiency is essential to extend the bearing service life in high-temperature environments. For heat evacuation, foil-side cooling is a very effective method. For more in-depth analysis of thermal characteristics of the foil bearing, a three-dimensional (3D) thermal-elasto-hydrodynamic (TEHD) coupling model of multi-leaf thrust foil bearing (MLTFB) with cooling channel is established in this paper. In view of the good heat transfer performance and more uniform gas velocity distribution in bionic flow channels, various bionic cooling channels of foil bearings are proposed and the structural parameters are optimized. The effects of cooling channel type, cooling channel width, span ratio, cooling gas supply mode, and rotational speed on the thermal and loading performance of foil bearings are investigated. The studies demonstrate that the spider net round cooling channel exhibits higher heat transfer performance and improved uniformity of temperature. Compared to the cooling gas supply from inner edge, the cooling gas supply from the outer edge proves to be more effective. The maximum temperature of lubricant gas film can be greatly reduced with wider cooling channels and a smaller channel span at the outer edge. The maximum temperature of lubricant gas film and bearing load are reduced as the Reynolds number of cooling gas increases. There exists an optimal Reynolds number that can achieve the highest uniformity of temperature.