Theoretical and experimental study is presented on temperature-tuned signal-resonated quasi-phase-matched optical parametric oscillator (OPO) in multi-grating periodically poled lithium niobate (PPLN) pumped by an acousto-optically Q-switched cw-diode-end-pumped Nd∶YVO4 laser. The continuously tunable signal output from 1369.7 nm to 1678.8 nm without wavelength overlap is demonstrated. The formula of calculating the signal wavelength as a function of the grating period and the temperature is given. The formula of calculating the temperature as a function of the signal wavelength and the grating period is also given. Based on those work, the relative temperature tuning ranges for each grating period to realize continuously tunable signal output without wavelength overlap can be calculated directly. So it does not need to solve simultaneous equations of energy and momentum conservation through point-by-point computation. In addition, the uniform deviation of the grating period in the whole periodically poled crystal from the ideal length is usually inevitable, as well as the random variation in the length of the domain. The method of correction computation on grating period is given by using the temperature tuning curve got in the experiment.