A design of microchip cooling with natural convection driven multi-phase coolant flows is proposed by using thermoelectric modules as heat sinks. A new multi-component multi-phase (MCMP) thermal energy transport model is built for convective heat transfer with solid–liquid–gas phase changes. Different from previous lattice Boltzmann models based on temperature distributions, the present model is based on MCMP energy density distributions, which track sensible and latent heat transport for each phase. The local MCMP heat fluxes are related to mesoscale relaxation times and phase volume fractions. Transient solid–liquid–gas interfaces and local temperatures are obtained through the dynamical balance of mesoscale forces and fluxes among all phases together with MCMP enthalpy–temperature distributions. Comparisons of the on and off states of the heat sink modules show that the chip temperature can drop from about 300 to 110 °C, with the coolant liquid–gas phase change temperature of 80 °C at equivalent heat source and sink intensities of 100 W/cm. Results also show that increasing heat sink intensity to 300 W/cm or decreasing gas–liquid phase change temperature to 60 °C can further decrease the chip temperature to 90 °C. The effects of sizes of chips, modules, and cooling units are also illustrated. It is observed that gas bubbles attached on chips impede heat transfer due to the low gas phase thermal conductivity, which means future improvements should also focus on removing or degrading attached gas bubbles. This model provides a quantitative tool for immersion chip cooling performances.