The combined use of Extreme Gradient Boosting (XGBoost) algorithm, one of the machine learning (ML) methods, and a generalization of Hermite-Biehler theorem to obtain a novel PID controller that will ensure robustly stable and optimized operation of a micro thermoelectric cooler (Micro-TEC), which is the main part of a Polymerase chain reaction (PCR) device, is a unique approach of our study compared to previous studies. Therefore, we first established a mathematical model of the micro-TEC by making real-time measurements and then, a new data set was created to find the optimum parameter values of PID controller, and finally, XGBoost Hyperparameters with GridSearchCV was used for the first time to predict PID controller parameters. The XGBoost algorithm achieved 97% training success and 91% test success in estimating the parameters of the PID controller. Moreover, the novel controller developed using the XGBoost algorithm in this study has an impressive speed of 3 seconds. Additionally, our proposed method was compared with various metaheuristic optimization algorithms in terms of error percentage. The error percentages of XGBoost, the equilibrium optimization, the particle swarm optimization and the artificial bee colony optimization algorithms were found to be 0.4%, 1.1%, 3.7% and 11.1%, respectively. It is observed the settling times of micro-TEC with ML-PID controller for all five PCR cycles are 4.86, 44, 83.4, 123 and 162.5 seconds, respectively, and the overshoot values are below 5%. The proposed method gave the smallest settling time, error and overshoot percentages compared to these metaheuristic optimization algorithms.