The material lost through stellar winds of asymptotic giant branch (AGB) stars is one of the main contributors to the chemical enrichment of galaxies. The general hypothesis of the mass-loss mechanism of AGB winds is a combination of stellar pulsations and radiative pressure on dust grains, yet current models still suffer from limitations. Among others, they assume chemical equilibrium of the gas, which may not be justified due to rapid local dynamical changes in the wind. This is important, as it is the chemical composition that regulates the thermal structure of the wind, the creation of dust grains in the wind, and ultimately the mass-loss by the wind. Using a self-consistent hydrochemical model, we investigated how non-equilibrium chemistry affects the dynamics of the wind. This paper compares a hydrodynamical and a hydrochemical dust-free wind, with focus on the chemical heating and cooling processes. No sustainable wind arises in a purely hydrodynamical model with physically reasonable pulsations. Moreover, temperatures are too high for dust formation to happen, rendering radiative pressure on grains impossible. A hydrochemical wind is even harder to initiate due to efficient chemical cooling. However, temperatures are sufficiently low in dense regions for dust formation to take place. These regions occur close to the star, which is needed for radiation pressure on dust to sufficiently aid in creating a wind. Extending this model self-consistently with dust formation and evolution, and including radiation pressure, will help to understand the mass-loss by AGB winds.