We numerically study the thermal stability properties of computer memory storage realized by a magnetic ellipse. In the case of practical magnetic random-access memory devices, the bit can form a spin texture during switching events. To study the energy barrier for thermally induced switching, we develop a variational procedure to force the bit to traverse a smooth path through configuration space between the points of stability. We identify textured configurations realizing domain-wall propagation, which may have an energy barrier less than that of the corresponding monodomain model. We contrast the emergence of such micromagnetic effects in thermal versus field-induced switching.