Understanding fusion mechanisms employed by SARS-CoV-2 spike protein entails realistic transmembrane domain (TMD) models, while no reliable approaches towards predicting the 3D structure of transmembrane (TM) trimers exist. Here, we propose a comprehensive computational framework to model the spike TMD only based on its primary structure. We performed amino acid sequence pattern matching and compared the molecular hydrophobicity potential (MHP) distribution on the helix surface against TM homotrimers with known 3D structures and selected an appropriate template for homology modeling. We then iteratively built a model of spike TMD, adjusting "dynamic MHP portraits" and residue variability motifs. The stability of this model, with and without palmitoyl modifications downstream of the TMD, and several alternative configurations (including a recent NMR structure), was tested in all-atom molecular dynamics simulations in a POPC bilayer mimicking the viral envelope. Our model demonstrated unique stability under the conditions applied and conforms to known basic principles of TM helix packing. The original computational framework looks promising and could potentially be employed in the construction of 3D models of TM trimers for a wide range of membrane proteins.