We study a temperature-aware scheduling problem aiming in maximizing the throughput of a set of unit-length jobs, each one having its own heat contribution, on a single processor operating under a strict temperature threshold. Following a simplified model for the processor’s thermal behavior, proposed by Chrobak et al.[9], we analyze the approximation factor of the natural CoolestFirst scheduling algorithm for jobs with common release dates and deadlines. We first prove a $\frac{k}{k+1}$ factor, where $k$ depends on a partition of the jobs according to their heat contributions. Next, we refine our partition and provide a linear program that shows a lower bound of 0.72 on the approximation factor.