When a suspension of colloidal particles is subjected to a strong electric or magnetic field, the induced dipolar interactions will cause the particles to form organized structures, provided a sufficient permittivity or permeability mismatch exists, respectively, between the particles and the suspending liquid. A uniaxial field will produce uniaxial structures, and a biaxial field, such as a rotating field, will produce biaxial structures, and either of these structures can be pinned by polymerizing the continuous phase to produce field-structured composites. We have previously reported on the coarsening of field-structured composites in the absence of thermal effects, i.e., Brownian motion. Athermal simulations are primarily valid in describing the deep quenches that occur when the induced dipolar interactions between particles greatly exceed k(B)T. However, deep quenches can lead to kinetic structures that are far from equilibrium. By introducing Brownian motion we have shown that structures with significantly greater anisotropy and crystallinity can form. These structures have enhanced material properties, such as the conductivity, permittivity, and optical attenuation. Careful anneals at certain fixed fields, or at continuously increasing fields, should produce more anisotropic structures than the deep quenches we have used to synthesize real materials.