\justifying The wet-to-dry transition of Mars is recorded by a changing distribution of rivers, which was interpreted as the result of a decorrelation between surface temperature and elevation with a thinner atmosphere. Here we use a climate model to re-examine the interpretation. We find that the weakening of the greenhouse effect, rather than atmospheric pressure, accounts for the decorrelation. The decorrelation happens near surface pressure $ \sim 0.1$ bar for a pure $\mathrm{CO_2}$ atmosphere, or longwave optical depth $\sim$ 1 for a gray gas. Under the weak greenhouse limit, the surface is mainly heated by insolation and thus surface temperature decorrelates with elevation. Under the strong greenhouse limit, the surface is mainly heated by the atmosphere, whose temperature is controlled by advection and convection over the lowlands. Our results suggest that the correlation between river distribution and elevation should be re-examined with different greenhouse forcings and a low atmospheric pressure.