We describe the critical design parameters and present detailed experimental and theoretical studies for efficient, continuous-wave (cw), single-pass second harmonic generation (SHG) based on novel cascaded multicrystal scheme, providing >55% conversion efficiency and multiwatt output powers at 532 nm for a wide range of input fundamental powers at 1064 nm. Systematic characterization of the technique in single-crystal, double-crystal and multicrystal schemes has been performed and the results are compared. Optimization of vital parameters including focusing and phase-matching temperature at the output of each stage is investigated and strategies to achieve optimum SHG efficiency and power are discussed. Relevant theoretical calculations to estimate the effect of dispersion between the fundamental and the SH beam in air are also presented. The contributions of thermal effects on SHG efficiency roll-off have been studied from quasi-cw measurements. Using this multicrystal scheme, stable SH power with a peak-to-peak fluctuation better than 6.5% over more than 2 hours is achieved in high spatial beam quality with M2<1.6.