We have proposed and demonstrated a nearly-noncritical phase-matched (NCPM) optical parametric oscillation (OPO) in an MgO:LiNbO3 crystal with 5 mol\% MgO by temperature tuning. By giving up perfect NCPM, the practical tuning range for the OPO is increased by two times. For the crystal, the operated temperature decreases with the phase-matching angle at degeneracy. With a cutting angle of 82 degrees instead of the noncritical case of 90 degrees, the tuning range was increased. In order to obtain a sufficiently high output pulse energy for both signal and idler throughout the entire tuning range, five sets of mirrors were used for the resonator. The tuning range of the OPO was 800 - 1700 nm with temperatures tuning from 83 degrees C to 224.2 degrees C. The output energy was about 6.45 mJ with a conversion efficiency of nearly 13\%. The bandwidth of the output was 1.0 - 1.1 nm.