## 1 Introduction  
Living organisms are a natural source of thermal radiation, which is the result of heat produced in many physiological processes. Body temperature is a very basic indicator, and deviations from normal levels can be a symptom of disease. Its measurement is an essential part of many diagnostic mechanisms. 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, we 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 we 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 us with additional input data for our 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].  
Our main goal is to demonstrate the power of multimodal ML tools for the non-invasive monitoring of physiological indicators as a crucial part of smart farming and veterinary control. The paper is organized as follows: Section two reviews the current state of research for farm animals physiological data acquisition and processing. In the third section, we describe the proposed method, including infrared thermography, the data collection stage, and some machine learning techniques that we use. Section four presents the results of our temperature estimation. They are discussed and summarized in the last part of the text, which outlines the most important conclusions and points to directions for further research.