A theory is proposed for estimation of linewidth of an ~20 kHz class dye laser transversally pumped by nanosecond pulse width pump lasers such as frequency doubled Q-switched Nd:YAG laser (λ ~ 532 nm) and copper hydrogen bromide laser (λ ~ 510 nm). The experimental results are explained on the bases of dye solution’s thermal and flow parameters obtained by computational fluid dynamics simulation and the proposed theory. The fusion of experimental investigations, computational fluid dynamics simulation and the proposed theory has led to establishment of an empirical relationship to predict the linewidth of the dye laser.