We investigate the dynamics of spreading of a small liquid droplet in gas in a one-component simple fluid, where the temperature is inhomogeneous around 0.9T{c} and latent heat is released or generated at the interface upon evaporation or condensation (with T{c} being the critical temperature). In the scheme of the dynamic van der Waals theory, the hydrodynamic equations containing the gradient stress are solved in the axisymmetric geometry. We assume that the substrate has a finite thickness and its temperature obeys the thermal diffusion equation. A precursor film then spreads ahead of the bulk droplet itself in the complete wetting condition. Cooling the substrate enhances condensation of gas onto the advancing film, which mostly takes place near the film edge and can be the dominant mechanism of the film growth in a late stage. The generated latent heat produces a temperature peak or a hot spot in the gas region near the film edge. On the other hand, heating the substrate induces evaporation all over the interface. For weak heating, a steady-state circular thin film can be formed on the substrate. For stronger heating, evaporation dominates over condensation, leading to eventual disappearance of the liquid region.