This paper investigates schedulability analysis for thermal-aware real-time systems. Thermal constraints are becoming more and more critical in new generation miniaturized embedded systems, e.g. Medicals implants. As part of this work, we adapt the PFPasap algorithm proposed in [1] for energy-harvesting systems to thermal-aware ones. We prove its optimality for non-concrete1 fixed-priority task sets and propose a response-time analysis based on worst-case response-time upper bounds. We evaluate the efficacy of the proposed bounds via extensive simulation over randomly-generated task systems.