The temperature acceptance bandwidth of second-harmonic generation (SHG) can be dramatically improved by using two different kinds of nonlinear crystals with opposite signs of temperature derivation of phase mismatch. We study two SHG processes for the existing 1064 and 1550 nm high-average-power lasers. The numerical results show that the temperature acceptance bandwidth for SHG at 1064 nm can be three to five times larger than that of traditional single-crystal design, and it is also larger than that of using temperature-insensitive yttrium calcium oxyborate crystal. Importantly, the proposed design is applicable to various wavelengths, which suggests its potential in high-average-power SHG applications.