Extending temperature acceptance bandwidth in second harmonic generation (SHG) by cascading nonlinear crystals is a simple and efficient method. Based on the dispersion of air, a formula describing how dispersion of air affect the conversion efficiency is derived. Based on the formula, conversion efficiency of SHG of 1064 nm in cascaded KTiOPO4 crystals versus temperature is simulated, and corresponding experiments are conducted. In the experiments, conversion efficient is cosine distribute versus the distance between two cascaded crystals, and when the phase mismatch caused by dispersion of air is integer times of 2π, the maximum conversion efficiency reaches 47.9%, which is 12.9% higher than the maximum conversion efficiency in a single KTP crystal, and the temperature acceptance bandwidth is 78 ℃, which is two times broader than that in a single KTP crystal. The theoretical analysis is in good agreement with the experimental results. The research conclusions are conducive to extending temperature acceptance bandwidth for nonlinear frequency conversion by cascading crystals.