Federated Learning (FL) is the most widely adopted collaborative learning approach for training decentralized Machine Learning (ML) models by exchanging learning between clients without sharing the data and compromising privacy. However, since great data similarity or homogeneity is taken for granted in all FL tasks, FL is still not specifically designed for the industrial setting. Rarely this is the case in industrial data because there are differences in machine type, firmware version, operational conditions, environmental factors, and hence, data distribution. Albeit its popularity, it has been observed that FL performance degrades if the clients have heterogeneous data distributions. Therefore, we propose a Lightweight Industrial Cohorted FL (LICFL) algorithm that uses model parameters for cohorting without any additional on-edge (clientlevel) computations and communications than standard FL and mitigates the shortcomings from data heterogeneity in industrial applications. Our approach enhances client-level model performance by allowing them to collaborate with similar clients and train more specialized or personalized models. Also, we propose an adaptive aggregation algorithm that extends the LICFL to Adaptive LICFL (ALICFL) for further improving the global model performance and speeding up the convergence. Through numerical experiments on real-time data, we demonstrate the efficacy of the proposed algorithms and compare the performance with existing approaches.