Quantifying performance of biomolecular circuit designs across different environmental conditions is a key step in assessing their robustness. It is generally unclear how robust this performance is to the important environmental variable of temperature. Here, we address this issue for a transcriptional negative feedback circuit design that can speed up the response time using a combination of simple computational methods and dynamic experimental measurements. We use a simple two-state model of gene expression to illustrate different ways in which temperature dependence of reaction rate parameters can propagate through to the functional output. Next, we extend this analysis to the response time of a transcriptional negative feedback circuit design. Finally, we present experimental results estimating how response time of a negative transcriptional feedback circuit depends on temperature. These results help to develop a framework for assessing how functional output of biomolecular circuit designs can depend on temperature.