Temperature variability has substantial socioeconomic impacts through its association with the frequency and severity of heat extremes. Under anthropogenic influence, climate models project seasonally-dependent amplifications of near-surface temperature variability over some sectors of the Southern Hemisphere, and robust positive trends have already been observed in recent decades. Here we show that the amplification of subweekly temperature variability simulated by the multi-model ensemble mean of the sixth phase of the Coupled Model Intercomparison Project (CMIP6) over South Africa, Australia, and South America is often substantially smaller than in reanalyses in recent decades, reaching a similar amplification only at the end of the 21st century due to a weaker amplification of subweekly variance generation efficiency. Analysis of a large model ensemble indicates that this discrepancy may be due to internal climatic variability suggesting that the recent rapid amplification seen in reanalyses may slow down or even temporarily reverse in the near future.