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This paper deals with robust heart rate detection intended for the in-car monitoring of people. There are two main problems associated with radar-based heart rate detection. Firstly, the signal associated with the human heart is difficult to separate from breathing harmonics in the frequency domain. Secondly, the vital signal is affected by any interference signal from hand gestures, lips motion during speech or any other random body motions (RBM). To handle the problem of the breathing harmonics, we propose a novel algorithm based on time series data instead of the conventionally used frequency domain technique. In our proposed method, a deep learning classifier is used to detect the pattern of the heart rate signal. To deal with the interference mitigation from the random body motions, we identify an optimum location for the radar sensor inside the car. In this paper, a commercially available Novelda Xethru X4 radar is used for signal acquisition and vital sign measurement of 5 people. The performance of the proposed algorithm is compared with and found to be superior to that of the conventional frequency domain technique.