Characteristics of microjet hydrogen diffusion flames stabilized near extinction are investigated numerically. Two-dimensional simulations are carried out using a detailed reaction mechanism. The effect of burner wall material, thickness, and thermal radiation on flame characteristics such as flame height and maximum flame temperature are studied. Results show that the flame stabilizes at lower fuel jet velocities for quartz burner than steel or aluminum. Higher flame temperatures are observed for low conductive burners, whereas the flame length increases with an increase in thermal conductivity of the burner. Even though thermal radiation has a minor effect on flame characteristics like flame temperature and flame height, it significantly influences the flame structure for low conductive burner materials. The burner tip and its vicinity are substantially heated for low conductive burners. The effect of burner wall thickness on flame height is significant, whereas it has a more negligible effect on maximum flame temperature. Variation in wall thickness also affects the distribution of H and HO2 radicals in the flame region. Although the variation in wall thickness has the least effect on the overall flame shape and temperature distribution, the structure near the burner port differs.