High-entropy ceramics (HEC) materials have gained significant attention for their unique composition and diverse properties. Low thermal conductivity (κ) makes them promising materials for high-temperature applications. However, predicting the thermal properties of HECs is challenging due to the complex nature of their atomic interactions. This project explores the use of machine learning (ML) techniques to discover new compositions of HEC materials with low κ. To achieve this, a dataset combining experimental κ values of 166 HECs and conventional ceramics at various temperatures (5 K-1832 K) is constructed. The input features are then generated based on chemical composition. In the next learning process, various nonlinear regression ML models, including Kernel Ridge Regression (KRR), Random Forest Regression (RF), Support Vector Regression (SVR), and eXtreme Gradient Boosting (XGBoost) are employed. As a result, the RF, KRR, and XGBoost exhibit excellent performance, achieving high R2 scores over 0.90. Additionally, the accuracy of this model was tested using new cases of four compounds, which was not seen for the model before, where a good matching between experimental and predicted κ of the new HECs was found. To gain further insights into the ML models, feature importance analyses are conducted to identify key compositional features that influence κ in HECs. As an application, ML models are leveraged to explore a large composition space and screen promising HECs (30,382) to find candidates with ultralow κ (<1 W m-1K-1) at room temperature. Among the screened HECs, the relationship between important features and the predicted κ is investigated. Size disorder is identified as an important feature in lower κ values of HECs. Overall, this study provides valuable insights into the thermal properties of HECs and demonstrates the efficacy of ML in HECs discovery and design. Accordingly, using the periodic table, compositional information, and ML models, the κ-temperature behavior of a huge number of HECs can be accurately predicted.