Understanding surface temperature is important for habitability. Recent work on Mars has found that the dependence of surface temperature on elevation (surface lapse rate) converges to zero in the limit of a thin $\mathrm{CO_2}$ atmosphere. However, the mechanisms that control the surface lapse rate are still not fully understood. It remains unclear how the surface lapse rate depends on both greenhouse effect and surface pressure. Here, we use climate models to study when and why “mountaintops are cold”. We find the tropical surface lapse rate increases with the greenhouse effect and with surface pressure. The greenhouse effect dominates the surface lapse rate transition and is robust across latitudes. The pressure effect is important at low latitudes in moderately opaque ($\tau \sim 0.1$) atmospheres. A simple model provides insights into the mechanisms of the transition. Our results suggest that topographic cold-trapping may be important for the climate of arid planets.