The observable properties of galaxies depend on both internal processes and the external environment. In terms of the environmental role, we still do not have a clear picture of the processes driving the transformation of galaxies. The use of proxies for environment (e.g. host halo mass, distance to the Nth nearest neighbour, etc.), as opposed to the real physical conditions (e.g. hot-gas density) may bear some responsibility for this. Here, we propose a new method that directly links galaxies to their local environments, by using spatial cross-correlations of galaxy catalogues with maps from large-scale structure surveys [e.g. thermal Sunyaev–Zel’dovich (tSZ) effect, diffuse X-ray emission, weak lensing of galaxies, or the cosmic microwave background (CMB)]. We focus here on the quenching of galaxies and its link to local hot gas properties. Maps of galaxy overdensity and quenched fraction excess are constructed from volume-limited Sloan Digital Sky Survey (SDSS) catalogues, which are cross-correlated with tSZ effect and X-ray maps from Planck and ROSAT, respectively. Strong signals out to Mpc scales are detected for most cross-correlations and are compared to predictions from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) and BAryons and Haloes of MAssive Systems (BAHAMAS) cosmological hydrodynamical simulations. The simulations successfully reproduce many, but not all, of the observed power spectra, with an indication that environmental quenching may be too efficient in the simulations. We demonstrate that the cross-correlations are sensitive to both the internal [e.g. active galactic nucleus (AGN) and stellar feedback] and external processes (e.g. ram pressure stripping, harassment, strangulation, etc.) responsible for quenching. The methods outlined in this paper can be adapted to other observables and, with upcoming surveys, will provide a stringent test of physical models for environmental transformation.