Nanowire heterostructures, such as core/shell nanowires and nanoparticle-decorated nanowires, are versatile building blocks for a wide range of applications because they integrate dissimilar materials at the nanometer scale to achieve unique functionalities. Our group has recently developed a simple and general sol-flame method that combines solution chemistry and rapid flame annealing to decorate nanowire arrays with other materials in the form of shells or chains of nanoparticles. In this report, we investigate the fundamental aspects of morphology control of the nanowire heterostructures synthesized by the sol-flame method. We use copper (II) oxide (CuO) nanowires decorated by cobalt (II,III) oxide (Co3O4) as a model system and study the effects of various solution parameters on the morphology of the decorated Co3O4. In a typical sol-flame synthesis, CuO nanowires are dip-coated with a cobalt salt precursor solution, then air dried, and subsequently heated in the post-flame region of a premixed co-flow flame at a typical temperature of 990 oC for only 5s. We find that the final morphology of Co3O4 on the CuO nanowires is closely connected to the properties of both the solvent and the cobalt salt in the cobalt-precursor solution. First, the gaseous products generated by solvent combustion are responsible for the formation of Co3O4 nanoparticle chains. The gases generated by the solvent combustion blow the cobalt salts radially outward from the nanowire as the cobalt salts precipitate and decompose to form Co3O4. Larger amount of gas generation leads to higher degree of Co3O4 nanoparticle branching. Second, when most of the solvent is removed before the flame annealing step, no Co3O4 nanoparticle chain, but a Co3O4 shell, is formed instead due to the lack of gas blowing effect. Finally, when a cobalt salt with high solubility in the solvent is used as a precursor, precipitation does not occur until most of the solvent has evaporated and combusted. Hence, a Co3O4 shell is formed again due to the lacking of gas blowing effect. We believe that the new understanding will facilitate the application of the sol-flame method for the synthesis of nanowire heterostructures with tailored morphologies to satisfy the needs of diverse applications such as catalysis, sensors, solar cells, Li-ion batteries and photosynthesis.