The debate over the early Martian climate is among the most intriguing in planetary science. Although the geologic evidence generally supports a warmer and wetter climate, climate models have had difficulty simulating such a scenario, leading some to suggest that the observed fluvial geology (e.g., valley networks, modified landscapes) on the Martian surface could have formed in a cold climate instead. However, as we have originally predicted using a single‐column radiative‐convective climate model (Ramirez, Kopparapu, Zugger, et al., 2014, https://doi.org/10.1038/ngeo2000), warming from CO2‐H2 collision‐induced absorption on a volcanically active early Mars could have raised mean surface temperatures above the freezing point, with later calculations showing that this is achievable with hydrogen concentrations as low as ~1%. Nevertheless, these predictions should be tested against more complex models. Here we use an advanced energy balance model that includes a northern lowlands ocean to show that mean surface temperatures near or slightly above the freezing point of water were necessary to carve the valley networks. Our scenario is consistent with a relatively large ocean as has been suggested. Valley network distributions would have been global prior to subsequent removal processes. At lower mean surface temperatures and smaller ocean sizes, precipitation and surface erosion efficiency diminish. The warm period may have been approximately <107 years, perhaps suggesting that episodic warming mechanisms were not needed. Atmospheric collapse and permanently glaciated conditions occur once surface ice coverage exceeds a threshold depending on collision‐induced absorption assumptions. Our results support an early warm and semiarid climate consistent with many geologic observations.