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An improved version of a previously developed mesoscopic model is used to simulate transients and thermal interactions during growth of equiaxed dendrites of a pure substance. The model is validated through comparisons with exact, analytical solutions and direct, fully resolved phase-field simulations. The issue of constancy in the selection parameter, sigma*, during transients is addressed in some detail. The model is first applied to realistically simulate previously performed microgravity experiments involving the growth of succinonitrile dendrites from a stinger inside a growth chamber. It is shown how the thermal interactions between the seed and the dendrite and between the growth chamber wall and the dendrite cause temporal variations in the dendrite tip velocities. Excellent agreement with microgravity measurements is obtained. A scaling relation is derived that provides the duration of the seed size effect during the initial transient. The model is also used to investigate the transients arising during the growth of two equiaxed dendrites towards each other. A scaling relation for the duration of the transient decay of the tip velocities is derived. Additional study is needed to fully understand cases where equiaxed grains interact early before a fully dendritic structure is established.