We discuss the physical processes that control the thermal structure of lightly ionized winds from cool protostars. We concentrate our attention on the hydrogen gas and examine the heating, cooling, and chemical processes that affect the neutral and ionic species of atomic and molecular hydrogen. Warm silicate dust may condense out of the cooling wind and may heat the gas through collisions. Singly ionized sodium atoms, which do not recombine for the mass-loss rates we consider, set a lower limit to the ionization fraction in the wind. Magnetic fields, which are presumed to accelerate the wind, couple directly to the ionic component of the gas and transfer momentum and energy to the neutral component through collisions. We find this process of ambipolar diffusion to be the dominant source of heat input to the gas. We also find that the rate of am bipolar diffusion heating is sensitive to the ionization fraction in the gas and that ambipolar diffusion can keep the gas temperature above 103 K within about 102 stellar radii. Stellar winds having larger mass-loss rates tend to have cooler temperatures. In most cases, the hydrogen in the wind remains atomic and little H2 is formed. The wind remains, however, a conducive environment for the formation of CO molecules.