Third harmonic (TH) generation inside air plasma filaments provides a simple method to convert near-infrared laser pulses in the UV range. Here, we report on the optimization of the third harmonic generation during filamentation in the parameter space of focusing geometry, gas pressure, and incident laser pulse energy. It is observed that, in the nonlinear filamentation regime, the TH yield is largely dominated by the geometrical focusing condition and gas pressure. Using ambient air as medium for filamentation, an optimal numerical aperture (NA) = 0.07 was found for laser pulse with peak power close and above the critical power for self-focusing. For more loose focusing geometry (NA < 0.047), reduction of the air pressure can improve the conversion efficiency. In this case, the spatial mode of the third harmonic was also found to be more uniform than in ambient air. With scanning pinhole and crossing-filaments methods, it is revealed that in the situation of optimized focusing geometry (NA = 0.07) the TH accumulates constructively along the filament and exits at its end. In contrast, for the loose focusing geometry, the destructive interference effect of the TH generated at the leading and trailing edges of the filaments decreases the TH yield efficiency. This study provides a practical guidance for efficient conversion of near-infrared femtosecond pulses to UV domain.