Results from a high resolution model of horizontally homogeneous radiative-convective equilibrium, Romps 2011. Left: equilibrium temperature profiles for 3 values of CO2 compared to an observed tropical profile. Right: the temperature differences compared to the response to doubling CO2 in an ensemble of CMIP3 global climate models.
As a moist parcel of air ascends it cools as it expands and does work against the rest of the atmosphere. If this were the only thing going on, the temperature of the parcel would decrease at 9.8K/km. But once the water vapor in the parcel reaches saturation some of this vapor condenses and releases its latent heat, compensating for some of the cooling (you get about 45K of warming from latent heat release when a typical parcel rises from the tropical surface to the upper troposphere). A warmer parcel contains more water vapor when it becomes saturated, so it condenses more vapor as it rises, and temperature decreases with height more slowly. That is, the moist adiabatic lapse rate, , decreases with warming.
To say something about the warming of the tropical atmosphere, rather than that of a moist adiabat, we need to argue that the tropical troposphere is close to a moist adiabat and remains close as it warms. The upper troposphere will then warm more than the lower troposphere. This is precisely what happens in our global climate models. The consistency or inconsistency of this prediction with observations, particularly the Microwave Sounding Unit (MSU) temperatures, is a long-standing and important issue A failure of the upper troposphere to warm as much as anticpated by this simple argument would signal a destabilization of the tropics — rising parcels would experience a larger density difference with their environment, creating more intense vertical accelerations — affecting all tropical phenomena involving deep convection. I like to refer to warming following the moist adiabat as the most “conservative” possible — having the least impact on tropical meteorology.