Long term climate change on early Mars is characterized by a shift in the spatial distribution of rivers and lakes. Geological datasets suggest earlier paleo-rivers prefer higher surface elevations compared to rivers that formed later (Kite, 2019). On the other hand, modeling work also suggest a transition of surface lapse rate that comes with atmospheric escape throughout the Martian history (Wordsworth, 2016). The surface lapse rate follows the atmospheric lapse rate, which is close to dry adiabatic, when the CO₂ atmosphere is thick, but decouples when the atmosphere is thin. Figuring out the surface temperature distribution on early Mars is critical, because it tells us where the water sources from ice/snowmelt would have been during warming episodes. We use the MarsWRF GCM to explore the transition of river-forming climates. We assume the atmosphere is CO₂-only, but allow additional greenhouse warming by a gray gas scheme. To simplify the relation between elevation and surface temperature, we set 0 obliquity and include simulations with both idealized topography and real topography. The range of surface pressure is between 0.01 bar and 2 bar. We use a surface energy budget framework to analyze outputs (Fig. 2). Under the framework, variations in surface emission LW_s correspond to surface temperature variations. We find greenhouse heating LW_a is the only term that scales with surface temperature under high P_CO2, in contrast to predictions from the previous literature that sensible heat SH was the cause of the regime transition (Wordsworth, 2016). This conclusion does not change with switching to realistic topography or switching CO₂ radiation to a gray gas scheme. Under the low P_s but high-optical-depth κ gray gas case, the surface lapse rate still follows the atmosphere, so the regime transition can be attributed to the evolution of greenhouse gases other than CO₂. In future, we will add a surface liquid water potential algorithm to link the surface energy balance to paleo-river observations. Assuming surface liquid water is formed during transient ice-melting period, surface liquid water potential can be calculated from the T_s and P_s distributions. The output will be compared with different historical epochs to find the best-fit scenario with both CO₂ and non-CO₂ greenhouse forcing.