The aim of the study was to assess the usefulness of IRT measurements of selected regions of interest (ROI), i.e., the eyeball and the nose of whippet dogs, before and after coursing competitions taking place in various environmental conditions, thereby enabling the assessment of well-being and the level of heat stress. The research was carried out over two different periods with different thermal humidity indexes (THIs). In the first period, the THI was 59.27 (Run 1), while in the second period, the THI was 63.77 (Run 2). The experimental subjects comprised 111 sighthound-type dogs—whippets—that were photographed with a thermal imaging camera to determine their eye temperature (ET) and nose temperature (NT). The average minimum and maximum eye temperatures were statistically lower after running in both measurements. Increased minimum and maximum nose temperatures were also demonstrated after both runs. The nasal temperature values were statistically higher for Run 2, for which the THI was higher, compared to Run 1. Eyeball temperature may be a marker of thermoregulation ability, regardless of the ambient temperature. The value of ETmax decreased on average by 2.23 °C and 0.4 °C, while NTmax increased uniformly by 2 °C after both runs. A correlation was found between the IRT measurements and physiological indicators.