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There are discrepancies between global climate models regarding the evolution of the tropical tropopause layer (TTL) and also whether changes in ozone impact the surface under climate change. We use a 1D clear-sky radiative-convective equilibrium model to determine how a variety of factors can affect the TTL and how they influence surface climate. We develop a new method of convective adjustment, which relaxes the temperature profile toward the moist adiabat and allows for cooling above the level of neutral buoyancy. The TTL temperatures in our model are sensitive to CO2 concentration, ozone profile, the method of convective adjustment, and the upwelling velocity, which is used to calculate a dynamical cooling rate in the stratosphere. Moreover, the temperature response of the TTL to changes in each of the above factors sometimes depends on the others. The surface temperature response to changes in ozone and upwelling at and above the TTL is also strongly amplified by both stratospheric and tropospheric water vapor changes. With all these influencing factors, it is not surprising that global models disagree with regard to TTL structure and evolution and the influence of ozone changes on surface temperatures. On the other hand, the effect of doubling CO2 on the surface, including just radiative, water vapor, and lapse-rate feedbacks, is relatively robust to changes in convection, upwelling, or the applied ozone profile.