To make the DLA model associate with more realistic processes of crystal growth, the authors construct and study a new model including the experimental variables required. Diffusion particles of multicomponents diffuse on the square lattice as in the DLA model; the aggregation perimeter contacts with a thermal bath of temperature T and the sticking probability P consists of a constant probability Pc and the thermal one Pt at a neighbouring site of the perimeter, as P=(1- alpha )Pc+ alpha Pt ( alpha is a parameter which includes the non-equilibrium-equilibrium tendency of the system). Pt is evaluated by the thermodynamic distribution of the Ising system including up to next-nearest-neighbour interactions and chemical potentials. The system has the possibility of phase transitions. They show the phase transitions, aggregation patterns, correlation functions, fractal dimensions, and so on.