Analysis of infant body temperature, environmental temperature and respiratory behaviour has become an important aspect of Sudden Infant Death Syndrome research. The application of engineering techniques as a means of providing research tools has been found to be beneficial for medical research. Signal processing techniques have been developed and applied to the analysis of physiological signals that have been collected from infants in the home environment. These techniques allow physiological signals to be analysed and correlated with the use of both time and frequency domain algorithms. Signals of several days duration are manipulated so they may be easily viewed and studied without the loss of significant information. Parameter evaluation of the fundamental frequencies of periodic signals and statistical parameter estimation of random signals have been employed to tease out trends from within the data. Analysis of physiological signals from sleeping infants has revealed hourly oscillations in their body temperatures that are highly correlated with their breathing rate and breathing rate interquartile range (variability). The oscillations appear to have the highest magnitude when the infant rectal temperatures are near to the mean rectal temperature value. Although some form of relationship between temperature and respiration is evident, insufficient information has been yielded by these signal processing techniques to divulge exactly what the relationship is. A mathematical model of the human thermoregulatory control system has been developed to investigate the behaviour of temperature regulation in infants. The model has been used to test the hypothesis that infant thermal control is inherently unstable. In this model, heat flow through the body tissues is calculated and the effect of bedding on heat loss is also considered. Automatic temperature regulation is achieved by negative feedback control of the metabolic rate, sweat rate and blood flow distribution in the model. Under physiologically normal conditions, the model shows oscillatory behaviour with a period of approximately one hour. Therefore, the model indicates that the temperature oscillations that have been observed in infants in the home environment, may be a direct result of a marginally stable or unstable thermoregulatory control system. The oscillations occurred when the model was operating just below the thermoneutral point. If the mean infant rectal temperature is assumed to be close to the thermoneutral point, then the model behaviour agrees closely with the data collected from infants. Evidence gathered from the behaviour of the thermoregulation model and from the signals collected from infants suggests that thermoregulation may be a dominant control system within the body, therefore, temperature may directly influence respiration. A mathematical model of the human infant respiratory control system has been developed to investigate the effect of body temperature on respiratory system behaviour during sleep and to test the hypothesis that the respiratory system is influenced directly by temperature and indirectly by thermoregulation. A multi-compartment model configuration is used to represent the carbon dioxide and oxygen stores within the body and a controller, sensitive to carbon dioxide and oxygen, adjusts the ventilation rate to complete a negative feedback control loop. Small changes in body temperatures were found to affect the steady state response of the respiratory model while the stability remained relatively unaffected. However, the respiratory model is highly sensitive to small amounts of noise added to blood flows, metabolic rate and arterial gas partial pressures. Therefore, the observed oscillations in infant breathing rate may be a direct effect of thermoregulation while the infant breathing rate interquartile range oscillations are probably induced by another mechanism.