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Flameless catalytic heaters are thermal systems in which the chemical energy of gaseous fuel converts into heat with zero NOx and low CO (≤ 10 ppm) emissions. Hence, they are called green heaters in the industry. These heaters benefit from a fibrous porous medium as support for catalyst nanoparticles. Pore structure has a significant effect on transport phenomena inside the porous medium. With the dramatic growth of computers, it is possible to study the impact of geometric detail on combustion phenomena. This study investigates the effect of fiber orientation and diameter on the temperature distribution and the reaction zone of CH4 catalytic combustion in the fibrous medium. As the fiber axis angle increases from 10° to 90°, the reaction zone moves 24.1% toward the reactor inlet, the maximum temperature increases by 69.7 °C, and its distribution becomes more non-uniform. Moreover, as the diameter of the fibers increased from 5 µm to 10 µm, the reaction site moved 29.8% toward the end of the reactor, the maximum temperature increased by 34.9 °C, and its distribution became slightly more uneven. The results showed how the diameter and orientation of fibers influence the performance of porous catalytic reactors. This issue should be considered, especially to increase the life of catalytic burners.