The effect of temperature on the reliability and performance of electrical components and integrated circuits warrants the inclusion of thermal considerations in the early stages of electronic system design. However, the many design parameters involved in the design of the package and the die or macro placement, along with the use of expensive thermal simulations, poses difficulty for conventional optimization algorithms. To overcome that hurdle, this work proposes an efficient Bayesian optimization algorithm which is demonstrated for two early-stage design problems. First, the proposed algorithm is used for the thermal-aware placement of macros with a variable aspect ratio. Second, the proposed Bayesian optimization algorithm is utilized in a two-stage process to optimize the die placement and the package design parameters of a multi-chip module.