A plume model applied to radiosonde observations and ERA5 reanalysis is used to assess the relative importance of lower tropospheric moisture and temperature variability in the convective coupling of equatorial waves. Satellite precipitation and outgoing longwave radiation (OLR) variability show little coherence with plume model estimates of lower tropospheric vertically integrated buoyancy, when zero-entrainment is prescribed. In contrast, precipitation and OLR are shown to vary coherently with when "deep-inflow" entrainment is prescribed, highlighting that entrainment of environmental air over a deep layer of the lower troposphere plays an important role in modifying the thermodynamic properties of convective plumes in the Tropics. Consistent with previous studies, moisture variability is found to play a more dominant role than temperature variability in the convective coupling of the Madden-Julian Oscillation (MJO), equatorial Rossby (ER) waves, and easterly waves (EW) over the ocean, while temperature variability is found to play an important role in the convective coupling of Kelvin (KW) and inertio-gravity (IG) waves. Large-scale variations in sub-cloud layer moist static energy play a relatively small role in the convective coupling of equatorial waves, which is most strongly impacted by moisture variations in overlaying portions of the boundary layer and the lower free troposphere for the MJO, ERs, and EWs over the ocean, and by lower free tropospheric temperature variations in KWs and IGs. Simulations of the E3SM V2 and a pre-operational prototype of NOAA GFS V17 are examined, the former showing unrealistically high coherence between precipitation and when zero-entrainment is prescribed, the latter a more realistic relationship.