We demonstrate a novel form of thermally-assisted hysteresis in the transfer curves of monolayer MoS2 FETs, characterized by the appearance of a large gate-voltage window and distinct current levels that differ by a factor of ∼102. The hysteresis emerges for temperatures in excess of 400 K and, from studies in which the gate-voltage sweep parameters are varied, appears to be related to charge injection into the SiO2 gate dielectric. The thermally-assisted memory is strongly suppressed in equivalent measurements performed on bilayer transistors, suggesting that weak screening in the monolayer system plays a vital role in generating its strongly sensitive response to the charge-injection process. By exploiting the full features of the hysteretic transfer curves, programmable memory operation is demonstrated. The essential principles demonstrated here point the way to a new class of thermally assisted memories based on atomically thin two-dimensional semiconductors.