Cellular events that execute life programs are ordered and reproducible, despite the noise and randomness underlying their biochemical reactions. The identification of the processes that ensure this robust operation is essential not only to uncover the salient design principles in organisms, but also to forward-engineer reliable genetic networks for biotechnological and therapeutic purposes. The use of feedback for noise reduction has been suggested as a recurring motif in genetic networks. In this work, we show that regulated degradation of proteins implements a negative feedback loop that enhances robustness against stochastic fluctuations and cellular noise. The analysis is carried out in the context of the bacterial heat shock response where the tight control of the amount of heat shock proteins is achieved through an intricate architecture of feedback loops involving the sigma(32)-factor. The sigma(32) regulates the transcription of heat shock proteins under normal and stress conditions. An essential feature of the heat shock response is a feedback loop regulating the degradation of sigma(32). We investigate the noise-rejection properties of this loop, therefore illustrating our point in a biologically plausible example.