This paper presents a new greedy heuristic to extend SAT Solvers when solving the Preemptive resource-constrained project scheduling problem (PRCPSP-ST). The heuristic uses domain-specific knowledge to generate a fixed order of variable selection. We also extend previous work into encoding PRCPSP-ST by providing an alternative upper bound. The heuristic was tested against VSDIS on the J12 dataset. These experiments show that it performed, on average, six times slower than VSDIS.