Sigmoidal isothermal semi-logarithmic survival curves are of two main types; starting with a downward and changing to upward concavity and vice versa. Both can be described by a variety of mathematical models having 3-4 adjustable parameters. The temperature dependence of these models' parameters can be described by empirical models, which account for the progressive change in the sigmoidal shape, including its disappearance at either high or low temperatures. If the temperature history of a heat-treated population of microbial cells or spores ('temperature profile') can be described algebraically, then there is a way to estimate the survival pattern under these non-isothermal conditions without invoking the traditional D and z values, which require forcing straight lines through the curved experimental data. The described method is based on the assumption that the local slope of the non-isothermal survival curve is that of the isothermal curve at the momentary temperature, at a time, which corresponds to the momentary survival ratio. It is similar to the method previously proposed for microbial populations with a 'power law' type isothermal survival curves, except that the time, which corresponds to the momentary survival ratio, is calculated either symbolically or numerically as a procedure incorporated in the governing differential equation. The method's capabilities are demonstrated with simulated survival curves under temperature histories that resemble thermal processing of foods. They include heating to different target temperatures and starting the cooling at different times.