The momentary rate of complex biochemical reactions and biological processes may depend not only on temperature (or an equivalent factor like pH or moisture contents) but also on the system's momentary state. Also, complex reactions and processes need not have a single 'energy of activation' and their 'kinetic order' is not always clearly defined. Thus, the progress of such a reaction or process is governed by time dependent kinetics whose description requires a departure from the traditional models, which are based on an analogy to simple chemical reactions. A general model that takes these considerations into account is demonstrated with simulated biochemical reactions under monotonic temperature increase and decrease and under regular and irregular temperature fluctuations. Its potential application to microbial growth and growth followed by decay is also demonstrated. The model is in the form of a cumbersome differential equation, which, nevertheless, can be solved by standard mathematical software. In certain cases, the same software can also be used to determine the process's basic kinetic parameters, and their temperature dependence, from experimental data obtained under non-isothermal conditions. This could simplify the study of fast reactions and processes, where shortening the come up and cooling times to insignificance, as required by the traditional isothermal analyses, is not a viable option.