Broiler respiratory rate (RR) in cage systems is a core physiological indicator of health and stress. However, real-time, non-invasive continuous RR monitoring is difficult in a high-density breeding environment, thereby limiting precise poultry health management. This study developed a feasible non-contact broiler RR measurement method to address this gap. The proposed method integrates infrared thermal imaging and phase-based video magnification (PBVM). Using cage-reared white-feathered broilers as subjects, we selected the thoracodorsal and tail regions as regions of interest (ROI), applied PBVM to amplify subtle respiratory-related body surface movements, and extracted RR features via the Fast Fourier Transform (FFT). Two validation experiments were conducted under controlled laboratory conditions. One was an RR dynamic monitoring experiment covering the entire life cycle (4 to 36 days), which analyzed video data of 198 individual quiet broilers. The other was a multi-gradient heat stress experiment with temperature increases of +2 °C, +4 °C, and +5 °C, and analyzed video data of 162 individual quiet broilers. The method achieved favorable measurement accuracy: in the whole-life-stage experiment, the mean absolute error (MAE) was 0.036 Hz, the mean absolute percentage error (MAPE) was 4.461%, and the coefficient of determination (R²) reached 0.961; in the heat stress experiment, the MAE was 0.042 Hz, the MAPE was 3.270%, and the R² reached 0.928. Linear regression analysis confirmed that healthy broiler RR decreased linearly with increasing age, and verified that RR showed a stepwise response to thermal challenge with a positive correlation between RR increase and temperature increment, accompanied by growth stage specificity. This study provides a feasible non-invasive approach for broiler RR monitoring, offering preliminary reference data for early heat stress detection and sustainable poultry production.