The properties of aggregates generated from an off-lattice, two-dimensional, particle-cluster aggregation model with dipolar interparticle interactions have been investigated. The fractal dimension seems to be a monotonically decreasing function of the temperature, between a definite value close to 1 at T=0 and the limit T¿8, corresponding to diffusion-limited aggregation of particles with no interaction. Temperature and dipolar interactions are introduced by means of a Metropolis algorithm. By analyzing the orientational correlation function, and what we call the orientation probability density of the direction of the dipoles on the clusters, an ordered state is found at low temperatures. This order diminishes when the temperature increases, due to the disorder induced by the fractal geometry of the aggregates. Our study is extended to the three-dimensional case. A disordered state is found even at T=0, and a remnant order is shown when analyzing related two-dimensional correlations.