Heat curing has been recognized as one of the strategies to mitigate the shrinkage of alkali-activated slag (AAS) mortar. However, the impacts of heat curing regime on the drying shrinkage and the compressive strength of AAS mortar remain unclear. Therefore, this paper investigated the performance of AAS mortars cured at three different temperatures and four different durations. The results show that the heat curing hinders the late-age strength development of AAS mortars, particularly for those with an insufficient curing duration. This is related to the retarded early alkaline reaction and the increased volume of coarse pores inside the mortars. Furthermore, increasing the curing temperature is more effective in mitigating the drying shrinkage of AAS mortars than extending the curing duration. The decrease of drying shrinkage is primarily attributed to the reduced viscous deformation during the drying process, although the heat curing tends to increase the effective capillary pore pressure.