The paper examines the temperature history of gas accreted by forming galaxies in smoothed particle hydrodynamics (SPH) simulations. It finds that about half of the gas follows the conventional picture of shock heating to the virial temperature of the galaxy potential well ($T \sim 10^6$ K) before cooling and condensing to form stars. However, the other half radiates its gravitational energy at much lower temperatures, typically $T < 10^5$ K, leading to a bimodal histogram of maximum gas temperatures. The "cold mode" of gas accretion, where gas radiates its gravitational energy at low temperatures ($< 10^5$ K), dominates for low-mass galaxies ($M_{\text{gal}} \lesssim 10^{10.3} M_{\odot}$ or $M_{\text{halo}} \lesssim 10^{11.4} M_{\odot}$), while the conventional "hot mode" (shock heating to $T \sim 10^6$ K) dominates high-mass systems. Cold accretion is often directed along filaments, allowing efficient gas extraction from large distances, while hot accretion is quasi-spherical. The transition between cold and hot modes occurs at a critical mass scale, consistent with theoretical and observational transitions in galaxy properties. The cosmic star formation rate (SFR) tracks the overall history of gas accretion, with a decline at low redshift driven by decreasing infall rates onto halos and longer cooling times within halos. The study also discusses the implications of these findings for the morphology-density relation and the cosmic star formation history.The paper examines the temperature history of gas accreted by forming galaxies in smoothed particle hydrodynamics (SPH) simulations. It finds that about half of the gas follows the conventional picture of shock heating to the virial temperature of the galaxy potential well ($T \sim 10^6$ K) before cooling and condensing to form stars. However, the other half radiates its gravitational energy at much lower temperatures, typically $T < 10^5$ K, leading to a bimodal histogram of maximum gas temperatures. The "cold mode" of gas accretion, where gas radiates its gravitational energy at low temperatures ($< 10^5$ K), dominates for low-mass galaxies ($M_{\text{gal}} \lesssim 10^{10.3} M_{\odot}$ or $M_{\text{halo}} \lesssim 10^{11.4} M_{\odot}$), while the conventional "hot mode" (shock heating to $T \sim 10^6$ K) dominates high-mass systems. Cold accretion is often directed along filaments, allowing efficient gas extraction from large distances, while hot accretion is quasi-spherical. The transition between cold and hot modes occurs at a critical mass scale, consistent with theoretical and observational transitions in galaxy properties. The cosmic star formation rate (SFR) tracks the overall history of gas accretion, with a decline at low redshift driven by decreasing infall rates onto halos and longer cooling times within halos. The study also discusses the implications of these findings for the morphology-density relation and the cosmic star formation history.