Coherent perfect absorption (CPA) is an interference process associated with the zeros of the scattering matrix of interest for optical computing, data processing, and sensing. However, the noise properties of CPA remain relatively unexplored. Here, we demonstrate that CPA thermal noise signals exhibit a unique property: they are orthogonal to the signals transmitted through the network. In turn, such property enables a variety of thermal noise management effects, such as the physical separability of thermal noise and transmitted signals, and "externally lossless" networks that internally host radiative heat transfer processes. We believe that our results provide a new perspective on the many CPA technologies currently under development.