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A thermally assisted writing procedure is proposed in a tunnel junction based magnetic random access memory cell. The magnetic layers of the tunnel junction are both exchange-biased with antiferromagnetic layers, the reference layer having a much higher blocking temperature than the storage layer. In the operating mode, a current pulse sent through the junction generates enough heat to raise the temperature of the storage layer above its blocking temperature, without affecting the pinning of the reference layer. The concept is demonstrated here for an isolated junction using an homogeneous external magnetic field.