Using optical measurements and simplified thermodynamic models, thermal and fluid dynamic properties of the flame jets near the ignition limit are analyzed in a methane-fueled and constant volume prechamber combustor. Two types of cooling effects act on the flame jet; one is named "the convection cooling" by the nozzle wall during passage through the nozzle, the other is named "the mixing cooling" due to the entrainment of cold mixture after issuing into the main chamber. Model analyses show that, near the ignition limit, the convection cooling causes the flame jet a moderate temperature drop of about 200 K, and that the mixing cooling leads to a drastic drop in the flame jet temporature of about 800 K. Therefore, it is confirmed that the ignition process by the flame jet is severely affected by the thermal effect. Reasurements of CH-emission intensity from the flame jet at the nozzle exit also indicate that there exists almost on flame kernels in the flame jet weth the nozzle diameter below the ignition limit. The increase in the nozzle diameter enhances the thermal and chemical activity of the flame jet and leads to the early ignition, which in turn shortens the effective time of the flame jet. The shorter the effective time of the flame jet becomes, the slower the burning process in the main chamber. It is considered that the combustion acceleration is due to the effect of the flame jet on the stirring and dispersion of heat and active species over the entire main chamber.