Galaxy groups are believed to be important sites of gas pre-processing in galaxies, which in turn impacts their stellar and morphological evolution.  As groups accrete more galaxies, the groups themselves become increasingly poor in neutral atomic hydrogen (HI), and more cluster-like.  Studies of compact groups suggest that gas processing through tidal interactions simultaneously depletes the cold gas in galaxies and contributes to the build-up of the warm-hot intragroup medium (WHIM) that is sometimes detected in X-rays.  I will present the results of stacking ROSAT All-Sky Survey images for a large sample of groups for which we have simultaneous HI data from the ALFALFA survey in an attempt to detect the build-up of the WHIM in intermediate mass groups M>10^13 M_Sun, where we begin to see the impact of the group environment on the HI content of their member galaxies.  With HI and X-ray observations together, the goal is to simultaneously trace the recent accretion of galaxies and groups, and build-up of the hot gas reservoirs in groups and clusters.