Despite the strong empirical evidence that feedback from radio AGN active galactic nuclei regulates the growth of the most massive galaxies, we are far from understanding how this feedback cycle operates. Feedback models generally require an AGN to be fueled by cooled or cooling gas, with accretion of cooled gas being favored by current theory and observations. However, there is little direct evidence of hot gas cooling to low temperatures. I will discuss how X-ray observations at high spatial and spectral resolution, as could be provided by an X-ray Surveyor mission, can be used to probe feedback between a radio AGN and its hot atmosphere. My primary focus will be on thermally unstable cooling of the hot gas, but I will also consider aspects of energy transfer to the gas.