Accurate prediction of energy consumption in district heating systems plays an important role in supporting effective and clean energy production and distribution in dense urban areas. Predictive models are needed for flexible and cost-effective operation of energy production and usage, e.g., using peak shaving or load shifting to compensate for heat losses in the pipeline. This helps to avoid exceedance of power plant capacity. The purpose of this study is to automate the process of building machine learning (ML) models to solve a short-term power demand prediction problem. The dataset contains a district heating network’s measured hourly power consumption and ambient temperature for 415 days. In this paper, we propose a hybrid evolutionary-based algorithm, named GA-SHADE, for the simultaneous optimization of ML models and feature selection. The GA-SHADE algorithm is a hybrid algorithm consisting of a Genetic Algorithm (GA) and success-history-based parameter adaptation for differential evolution (SHADE). The results of the numerical experiments show that the proposed GA-SHADE algorithm allows the identification of simplified ML models with good prediction performance in terms of the optimized feature subset and model hyperparameters. The main contributions of the study are (1) using the proposed GA-SHADE, ML models with varying numbers of features and performance are obtained. (2) The proposed GA-SHADE algorithm self-adapts during operation and has only one control parameter. There is no fine-tuning required before execution. (3) Due to the evolutionary nature of the algorithm, it is not sensitive to the number of features and hyperparameters to be optimized in ML models. In conclusion, this study confirms that each optimized ML model uses a unique set and number of features. Out of the six ML models considered, SVR and NN are better candidates and have demonstrated the best performance across several metrics. All numerical experiments were compared against the measurements and proven by the standard statistical tests.