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. medical implants. As part of this work, we adapt the $PFP_{ASAP}$ algorithm proposed in \cite{Abdeddaim2013} for energy-harvesting systems to thermal-aware ones. We prove its optimality for non-concrete fixed-priority task sets and propose a response-time analysis based on worst-case upper bounds. We evaluate the efficacy of the proposed bounds via extensive simulation over randomly-generated task systems.