When the health condition changes, the amount of heat produced in the body usually responds. The blood flow carries some of this heat to the surface layers of the tissues, where it is released into the surrounding space through the processes of heat exchange. Its realization, however, depends strongly on the temperature and humidity characteristics of the surrounding environment. Therefore, one complex indicator is introduced to characterize the environment, the so-called temperature-humidity index (THI). Nowadays, there are many devices that measure this indicator. In order for normal heat exchange to take place, THI must be within some permissible limits. Beyond these limits, the normal heat exchange with the surrounding environment is disturbed and the body temperature cannot be considered an objective indicator for the health condition anymore. In addition, researchers consider two more basic parameters which provide information about the physiological state of dairy cows; namely, the pulse and the respiration rate. The problem that reswearchers focus on in the present research is in estimating the unknown rectal temperature of the animals based solely on these data and infrared images, without any intrusive procedures. The paper proposes the use of machine learning for the joint processing of multimodal data. Three different models are used to estimate rectal temperatures. Each one of them receives a plausibility score, determining its weight in the final prediction. Infrared thermography (IRT) allows for monitoring of the surface temperature distribution. The animals are periodically photographed without disturbing their daily routine. These IR images provide researchersus with additional input data for researcher'sour regression models. Its non-invasiveness makes it both harmless to the animal and cost-effective to the farmer. In this way, it allows for the continuous monitoring of physiological parameters and using the gathered data for scientific research. It also enables working from a sufficient distance, without introducing additional stress to the animal. These qualities make it a promising tool in veterinary medicine research ^{[1][2][3][4][5][6][7]}[1,2,3,4,5,6,7].

With the rapid growth of computational power and data transfer capabilities, machine learning (ML) and artificial intelligence (AI) are also making inroads into animal husbandry and veterinarian research. In particular, IRT is being increasingly used for health monitoring and the diagnosis of dairy cows, especially in studies related to heat stress, which causes severe losses, helping reusearchers analyze its effects on nutrition, milk production, reproduction, etc. There is plenty of evidence for the potential benefits of using IRT for monitoring udder health status in dairy cows and for the early detection of mastitis ^{[8][9][10][11][12][13][14][15][16]}[8,9,10,11,12,13,14,15,16]. Its role in detecting hoof lesions and lameness has also been reported ^[17][18][19][17,18,19]. The growth of the population and the increase of quality standards has set a requirement for the production of more and better quality food. The capabilities and potential benefits of IRT make systems for the automatic collection and processing of thermographic information and decision-making particularly important [20]. Some studies use computer vision technology and IRT to detect hoof diseases in dairy cows (see [21]). Others resort on deep learning methods, and more precisely, convolutional neural networks (CNNs), for detecting mastitis in dairy cows based on infrared images ^[22][23][24][22,23,24]. The possibility of using a combination of visible and infrared imaging has also been explored; for instance, to automate the measurement of pig skin surface temperature, emphasizing once more on the benefits of non-invasive methods [25]. The expansion of ML and AI into modern farming practices is facilitated by the advancement of increasingly more precise and affordable sensors reacting to subtle changes in the environment and the animals’ physiological parameters. This provides new opportunities for data analysis and ML-based optimization, which is the leading idea of ’smart farming’. There are many directions for development of this modern research field, but researchers shall focus on non-invasive diagnostics, allowing for precise real-time monitoring of the animals’ health condition without disturbing their comfort and exposing them to unnecessary stress. Body temperature is one of the most important physiological parameters to keep track of, and there are abundant data for it. Hence, multi-regression models predicting the rectal temperature are quite promising for the improvement of health conditions in animal farms and their overall optimization. Although the research area is relatively new, such studies have been conducted before, using different methods ^{[26][27][28][29][30][31][32]}[26,27,28,29,30,31,32] and technologies ^[33][34][33,34], leading to different conclusions. Researchers rely a lot on thermal images, like in ^[35][36][35,36], but researchers feed them into a multimodal algorithm along with tabular features, which improves the accuracy significantly. These ML models have become popular only in recent years due to their complexity, but with modern AutoML tools, they are already a standard task for data scientists ^[37][38][37,38]. The development of algorithms for processing information from multiple sensors began in the late 1980s, when the field of data fusion emerged [39]. Its aims to increase the accuracy of the assessment and reliability of the information system in case one of its sensors fails, to obtain a more accurate picture of the observed event or process, and to expand the area of observation. Multi-model approaches have become necessary in cases where the systems under evaluation may have different modes of operation (changing dynamics), each corresponding to a different model. The main advantage of this approach is its extreme robustness, which naturally comes at the cost of a higher computing load due to processing several models simultaneously. In the great variety of multi-model approaches [40], the algorithm of interacting multiple models [41] has emerged as one of the most successful. Stacking methods emerging in the 1990s; however, they became more popular in machine learning algorithms for various reasons (see ^[42][43][42,43]). They rely on weighted ensembles of models, rather than alternative choices. In this way, the imperfections of each individual ML algorithm tend to cancel out to some extend, and the overall variance of the result is reduced. There is plenty of research on the applications of artificial intelligence in improving health conditions and quality of life in animal farms [44], thus optimizing the food production and minimizing the cost. Some authors study the behavioral response, while others focus on the early detection of diseases or environmental monitoring [45]. The data are collected with interconnected sensors, and advanced algorithms are used for processing and analysis. Remote monitoring systems, combined with recognition and identification techniques powered by AI algorithms, are aimed at obtaining better assessments of crucial physiological parameters and characteristics of the environment, in particular, discovering deviations in the health status [46]. Food production is increasingly demanding and leads to new fields of applied science, such as precision agriculture and intelligent animal husbandry [47]. Global changes in the climate and extreme weather conditions also contribute to the stress in farmed animals. This has negative impacts on the quality and quantity of milk produced in farms, as recent studies reveal [48]. The digitalization of agriculture and the advent of modern technology facilitate the expansion of AI into animal husbandry. Cattle identification methods no longer rely just on radio frequencies, but uses image recognition techniques as well. Behavioral research applications are being created as an aid for disease prevention and the early detection of health issues, as well as may other diverse farming applications [49].