We propose the method for broadening the angular acceptance bandwidth of quasi-phase-matched (QPM) frequency doubling by using nearly ideal temperature QPM (NIT-QPM). By NIT-QPM we mean that the crystal temperature is not controlled at the temperature, which satisfies the collinear phase matching condition and is termed ideal temperature, but near it. The scalar analysis on periodically poled MgO doped of stoichiometric lithium tantalate (PP-MgO: SLT) second-harmonic generation (SHG) shows that, for single-pass extracavity frequency doubling, the angular acceptance bandwidth of NIT-QPM with a lower temperature would be greater than that of ideal temperature QPM (IT-QPM) which is usually used. In the experiment, the angular acceptance bandwidth of PP-MgO: SLT SHG is broadened from 4.6° to 6.4° when the heating oven temperature falls from the ideal temperature to a lower temperature.