Changes in lighting accompany modern urbanization trends and can lead to various pathologies based on circadian disturbances. In this study, we assessed the changes in the circadian rhythm of core body temperature (Tcore) and locomotor activity of Wistar-Kyoto rats (WKY) and spontaneously hypertensive rats (SHR) following exposure to different lighting conditions: extended light phase of the day (16 h–8 h, 20 h–4 h, 24 h–0 h), light pollution, monochromatic light, and bright light therapy. The telemetry data was collected after experimental lighting conditions during periods with standard lighting (12 h of light and 12 h of darkness) and was processed using linear and cosinor analysis. The daily rhythms of rats’ parameters persisted in accordance with the standard lighting regime. Tcore changes were observed in both groups compared to the initial period: in WKY, a decrease in Tcore during the darkness and an increase during the light; in SHR, the opposite trend, with Tcore increased during the darkness and decreased during the light phase of the day. A relationship between Tcore and activity was observed with weak correlation. WKY exhibited more pronounced signs of adaptive variation and desynchronization compared to SHR, which could be associated with a wider range of functional capabilities of the organism without cardiovascular pathology.