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Abnormal respiratory rate has been an important predictor of potentially serious clinical events such as cardiac arrest and admission to an intensive care unit (ICU). Inspite of this, the level of documentation of respiratory rates in many hospitals is poor, even when the patient's primary problem is a respiratory condition. This paper describes the development of a microcontroller based intelligent system to compute and keep a continuous real-time track of the respiratory rate of the patient under surveillance. Upon exceeding the boundaries of lower or upper safe respiratory rate limit, it triggers an alarm, and sends an SOS request via SMS to the concerned physician's cell-phone. The system employs smart temperature sensors that give continuous temperature feedback of the inhaled and exhaled air. The principle used in the development of the system is to keep a track of the amplified voltage difference (differential amplification) between two temperature sensors corresponding to exhalation and normal air temperature. A microcontroller computes the time period of breathing on a continuous basis, by recursively running an algorithm to detect maxima(s) and minima(s) in the real-time breathing plot and extracting its periodicity. The system has been designed to be inexpensive, portable and user friendly for applications in developing countries. The system was successfully tested on a range of patients of varying age and gender in different physical conditions and verified by a physician.