Bayesian Optimization has been successfully applied to find global optima of functions which are expensive to evaluate and without access to gradient information. Adaptive Bayesian Optimization extends it to dynamic problems where the functions over some space are assumed to evolve in a temporal dimension with temporally evolving optima. This requires the surrogate model used in Adaptive Bayesian Optimization to extrapolate correctly and accurately track optima with a minimum number of function evaluations. We propose to use Gaussian processes with a spectral mixture kernel to model the temporal dimension to accurately extrapolate and predict the optima. Spectral mixture kernel considers a mixture of Gaussian spectral density function which helps in quality extrapolation. We show the effectiveness of the proposed approach not only to various synthetic problems but also on a real-world problem of click-through rate prediction in an online learning setting. The experimental results demonstrate the superior performance of the proposed approach for Adaptive Bayesian Optimization. © 2020, Springer Nature Switzerland AG.