The accurate prediction of indoor air temperatures is vital for the timely control of thermal environments in livestock buildings. However, ensuring the accuracy of air temperature predictions is challenging due to the uncertainty introduced by external factors and periodic fluctuations. New approaches are required to improve the prediction accuracy of models for indoor air temperatures. A discrete model is developed that incorporates time-period groups (TPGs), the group buffered rolling (GBR) mechanism, and TPG factors. The measured temperature data were divided into four TPGs in chronological order, and the GBR mechanism with TPG factors eliminated fluctuations and periodicity from the time-series data. The efficacy of the proposed model was verified by comparing its results with those of two existing models (the grey model and discrete grey model) and filed experiments in layer hen houses. The traditional model only reflected the increasing trend of original air temperature data, but did not reflect periodic fluctuations. The mean absolute percentage error (APE) was >10% in the traditional model. The GBR mechanism and TPG factors allowed the new model to reflect deviations in the original time-series at each time point in real-time, thus minimizing the APE and improving the prediction performance. The modified model was superior to the traditional models, exhibited higher accuracy and reliable performance (APE < 10%), and accurately captured the periodic fluctuations in air temperature. It is a helpful tool for predicting indoor air temperatures, and may help in the development of improved control strategies for the indoor thermal environment. • A new discrete grey model modified with the group buffered rolling mechanism. • The GBR-DGM shows improved prediction performance for indoor air temperature. • Accurately predicts temporal fluctuations in air temperatures in a layer hen house. • Applications include the development of improved environmental control systems.