To present time-varying evidence, cumulative meta-analysis (CMA) updates results of previous meta-analyses to incorporate new study results. We investigate the properties of CMA, suggest possible improvements and provide the first in-depth simulation study of the use of CMA and CUSUM methods for detection of temporal trends in random-effects meta-analysis. We use the standardized mean difference (SMD) as an effect measure of interest. For CMA, we compare the standard inverse-variance-weighted estimation of the overall effect using REML-based estimation of between-study variance [tau[superscript 2]] with the sample-size-weighted estimation of the effect accompanied by Kulinskaya--Dollinger--Bjørkestøl ("Biometrics." 2011; 67:203-212) (KDB) estimation of [tau[superscript 2]]. For all methods, we consider Type 1 error under no shift and power under a shift in the mean in the random-effects model. To ameliorate the lack of power in CMA, we introduce two-stage CMA, in which [tau[superscript 2]] is estimated at Stage 1 (from the first 5-10 studies), and further CMA monitors a target value of effect, keeping the [tau[superscript 2]] value fixed. We recommend this two-stage CMA combined with cumulative testing for positive shift in [tau[superscript 2]]. In practice, use of CMA requires at least 15-20 studies.