A theoretical analysis of the ignition of a liquid fuel vapor-air mixture by a moving small source of heating was performed. A gas-phase model of the ignition with consideration given to heat transfer, liquid fuel evaporation, diffusion and convective motion of fuel vapor in the oxidizer medium, crystallization of the heating source, kinetics of the vaporization and ignition processes, temperature dependence of the thermophysical characteristics of the interacting substances, and character of motion of the heating source in the vapor-gas mixture was developed. The values of the ignition delay time τd, the main characteristic of the process, were determined. It was established how τd depends on the initial temperature, heating source sizes, velocity and trajectory of the heating source, and ambient air temperature.