Computational study of nanosecond pulse laser radiation in periodically poled LiNbO3 (PPLN) crystals reveals the complex spatio-temporal evolution of the 1.064 mu m fundamental harmonic (FH) and second harmonic (SH) energy fields with associated temperature fields, leading to the thermal dephasing and inhibition of second harmonic generation (SHG). The investigated range of the laser input power is W-0=0.5-50 W (with the pulse energy Q(0)=0.01-1 mJ/pulse and repetition rate of 50 kHz). For input laser powers W-0> 10 W the FH and SH energy fields are found to strongly couple with nonuniform temperature field, leading to significant thermal dephasing and SHG efficiency loss. Heat generation and temperature distributions also exhibit very significant nonuniformities along and across the laser beam, maximizing at the rear or inside the crystal, depending on the input power. However, conformal temperature tuning along the operating crystal inhibits these nonuniformities, and significantly enhances SHG efficiency under high input powers. For instance, selected PPLN conformal cooling parameters lead to the formation of a temperature-uniform quasi-phase-matching channel for a 300 mu m diameter laser beam providing a high SHG efficiency (approximate to 64%) at 20 W input power. (c) 2005 American Institute of Physics.