Heart rate is one of the most crucial vital signs and can be measured remotely using microwave Doppler radar. As the distance between the body and the Doppler radar sensor increases, the output signal weakens, making it difficult to extract heartbeat waveforms. In this study, we propose a new template-matching method that addresses this issue by simulating Doppler radar signals. This method extracts the heartbeat waveform with higher accuracy while the participant is naturally sitting in a chair. An extended triangular wave model was created as a mathematical representation of cardiac physiology, taking into account heart movements. The Doppler radar output signal was then simulated based on this model to automatically obtain a template for one cycle. The validity of the proposed method was confirmed by calculating the PPIs using the template and comparing their accuracy to the R-R intervals (RRIs) of the electrocardiogram for five participants and by analyzing the signals of eight participants in their natural state using the mathematical model of heart movements. All measurements were conducted from a distance of 500 mm. The correlation coefficients between the RRIs of the electrocardiogram and the PPIs using the proposed method were examined for five participants. The correlation coefficients were 0.93 without breathing and 0.70 with breathing. This demonstrates a higher correlation considering the long distance of 500 mm, and the fact that body movements were not specifically restricted, suggesting that the proposed method can successfully estimate RRI. The average correlation coefficients, calculated between the Doppler output signals and the templates for each of the eight participants, exceeded 0.95. Overall, the proposed method showed higher correlation coefficients than those reported in previous studies, indicating that our method performed well in extracting heartbeat waveforms. Our results indicate that the proposed method of remote heart monitoring using microwave Doppler radar demonstrates higher accuracy in estimating the RRI of the electrocardiogram while at rest sitting in a chair, and the ability to extract the heartbeat waveforms from the measured Doppler output signal, eliminating the need to create templates in advance as required by conventional template matching methods. This approach offers more flexibility in the measurement environment than conventional methods.