Crystallization at the margin of a quiet cooling magma has been studied numerically, taking into account the kinetics of crystalligation. The variables are the latent heat value, the growth and nucleation functions, the initial magma temperature, and the thermal contrast between magma and country rock. We have investigated a wide range of values for these parameters corresponding to natural conditions. We show that after a highly transient stage, crystallization tends toward an equilibrium between heat production (latent heat release) and heat loss. Given the small diffusivity of country rocks, latent heat release is the main factor controlling the temperature evolution. In order to minimize the latent heat release, crystallization occurs at a temperature where nucleation is small. This can be close to either the liquidus or the solidus, depending on the initial conditions. The main process controlling crystallization is nucleation and not crystal growth. Nucleation occurs as a series of sharp pulses followed by longer periods of crystal growth. The nucleation pulses give birth to thermal oscillations. These oscillations can be sustained if the interior magma temperature is above the liquids independently of the heat loss mechanism. We show that the phenomenon occurs on the scale of a few centimeters which corresponds to the inch-scale layering of many ultrabasic complexes. The model allows us to calculate crystal sizes which are in good agreement with geological observations. The crucial parameters which determine crystal size variations near the margins of igneous bodies are the initial thermal conditions as well as the nucleation and growth functions. In the main cooling regime close to the liquidus, significant size variations can be created by small thermal disturbances.