Micro-explosive breakup of heterogeneous liquid droplets can enhance controlled secondary atomization in specific areas of reactors, combustion chambers, heat exchangers, and mixers. To apply this mechanism in various practical applications, it is necessary to identify conditions when child droplets have predictable sizes. Available models of micro-explosive breakup can describe the processes in a heterogeneous droplet until its destruction with high accuracy and considerable detail. This study presents a mathematical model to predict the number and sizes of child droplets in the micro-explosive breakup of two-component droplets. A comparison of mathematical modeling results with experimental data indicated that they are in good agreement (with no more than a 10% deviation). The initial problem statement was refined with respect to geometry, the number of variables considered, effects, and processes. Given the required computational resources, a parametric analysis was conducted to investigate the impact of a selected set of variables on the characteristics of the child droplets. Due to practical limitations, it would be challenging to assess these features through experimental means. These factors include the shift of the water core relative to the center, nonsphericity of droplets, droplet sizes up to dozens of micrometers, etc. These factors are particularly relevant to liquid and composite fuel spraying equipment in engines and propulsion systems.