A well-known process used to produce recyclable polymer films by stretching is machine direction orientation (MDO). During the drawing stage of MDO, a semicrystalline morphology is developed, which ultimately determines the final properties of the film. Predicting this morphology is demanding, as it is affected by numerous factors such as the strain rate, the temperature, the molecular weight of the drawn polymers, and its distribution. Atomistic simulations are valuable for studying the development of semicrystalline morphology upon stretching, as they can shed light on crystal nucleation and growth and their dependencies on molecular characteristics and processing conditions. In this work, beginning from linear monodisperse polyethylene melts of high molecular weight, we perform molecular dynamics drawing simulations. Applying a planar extension protocol that mimics the drawing stage of a real MDO process, we investigate the dependence of the developed semicrystalline morphology on the strain rate and on temperature. In particular, using a homebuilt algorithm to estimate the evolution of the degree of crystallinity over time and applying a mean first-passage time analysis, we show that increasing the strain rate affects both crystal nucleation and growth mechanisms, accelerating the development of the semicrystalline morphology. On the other hand, a more complicated dependence on temperature is found. At deep supercoolings, crystal growth is rate-controlling, whereas at high temperatures, crystal nucleation is limiting. As a consequence, an optimal temperature where the overall crystallization rate exhibits a maximum is found. Our results are compared against experimental data available in the literature, and a very good qualitative agreement is found. Finally, we develop a theoretical model for both the strain rate and temperature dependence of PE nucleation. Beginning from the simple geometric idea that a crystal nucleus can be envisaged as a cylindrical bundle and assuming a purely elastic response to deformation up to the induction time, we extract useful relations for the critical nucleus size and the nucleation rate as functions of the temperature and the strain rate that provide an accurate description of our simulation results.