We derive coarse-grained models of polyethylene in the melt state with the aim to study polymer crystallization. This requires a low level of coarse-graining: We use a mapping of two CH2 groups onto one bead. The coarse-grained beads are connected with harmonic springs, an optimized angular potential, and an optional torsional potential. Coarse-grained potentials are derived from detailed all-atom simulations, and an optimized form of the force field is then derived which achieves a good accuracy in reproducing the static properties of the chains. We address the question over which temperature range such models can be used, and in particular if the model is capable of reproducing the phase transition to an ordered state; it is found that the qualitative behavior of short polyethylene chains is well described, and the experimental melting temperature of C44H90 is approached when using the most accurate optimized model.