I discuss the thermal structure of a wind that is centrifugally driven from the surface of a protostellar disk. A generalized version of the Blandford & Payne self-similar wind model is introduced, and the temperature and ionization distributions in the outflow are investigated. Focusing on the evolution of atomic winds, the heat equation and the rate equations that describe the ionization and excitation state of hydrogen are solved self-consistently. I find that ambipolar diffusion is a robust mechanism for heating the gas. The heating rate is a sensitive function of the ionization fraction in the gas, and a strong feedback mechanism exists between the gas temperature and the gas ionization state. As a result of this, temperatures of the order of 10(4) K and ionization fractions approximately 0.1-1 are established at distances of approximately 10(2)-10(3) AU from the central star. The Balmer-continuum photoionization of hydrogen atoms is of little importance in these outflows, but the UV radiation field generated in the accretion process is strong enough to ionize Na I and C I, providing good coupling between the neutral and the charged components at the base of the flow. In the more powerful outflows, molecular hydrogen is collisionally dissociated close to the disk surface, and hydrogen is mainly atomic within a few astronomical units, from the central source. It also demonstrate that these outflows have enough momentum to lift dust grains from the disk surface. The implications of these findings for the line and continuum emission properties of T Tauri stars are discussed in the subsequent papers of this series.