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Among various stream temperature models those based on nonlinear regression frequently attract attention due to their simplicity and small number of required variables. Among such approaches the logistic regression model developed twenty years ago for weekly data is still widely used in various scientific studies that require quick and simple calculation of stream water temperature. The model has been modified a number of times in recent years to capture the relationship between daily stream water temperatures, air temperatures and discharge. In this study, we propose further modifications of the logistic regression model that do not require any additional variables that may be hard to measure. The proposed models capture the relationship between the stream temperature and the declination of the Sun, the air temperature and the discharge from a number of recent observations. The proposed approaches are tested on six rivers located in diverse orographic conditions of temperate climate zones of Europe and USA. Although the proposed models remain very simple, their performances are competitive against the performances of more advanced semi-physical or data-driven models.