This paper investigates the effect of a controlled cooling rate on magnetic field reversal assisted by spin transfer torque (STT) in thermally assisted magnetic random access memory. By using a gradual linear decrease of the voltage at the end of the write pulse, the STT decays more slowly or at least at the same rate as the temperature. This condition is necessary to make sure that the storage layer magnetization remains in the desired written direction during cooling of the cell. The influence of the write current pulse decay rate was investigated on two exchange biased synthetic ferrimagnet (SyF) electrodes. For a NiFe based electrode, a significant improvement in writing reproducibility was observed using a gradual linear voltage transition. The write error rate decreases by a factor of 10 when increasing the write pulse fall-time from similar to 3 ns to 70 ns. For comparison, a second CoFe/NiFe based electrode was also reversed by magnetic field assisted by STT. In this case, no difference between sharp and linear write pulse fall shape was observed. We attribute this observation to the higher thermal stability of the CoFe/NiFe electrode during cooling. In real-time measurements of the magnetization reversal, it was found that Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling in the SyF electrode vanishes for the highest pulse voltages that were used due to the high temperature reached during write. As a result, during the cooling phase, the final state is reached through a spin-flop transition of the SyF storage layer. (C) 2015 AIP Publishing LLC.